Bayern Munich exacted some revenge on Freiburg and maintained their two-point lead on Borussia Dortmund at the Bundesliga summit with a 1-0 win at Europa-Park Stadion.

Thomas Tuchel's side were eliminated from the DFB-Pokal by Freiburg on Tuesday, but they dug deep four days on to remain on course for an 11th successive domestic title.

Matthijs de Ligt gave Bayern the key breakthrough six minutes into the second half with a thunderous long-range strike, either side of some fine goalkeeping from Mark Flekken.

Fourth-place Freiburg had been unbeaten in seven league games, but they were unable to respond as Bayern made it back-to-back league wins since Tuchel took charge.

Flekken was kept busy in the Freiburg goal in a lively – albeit goalless – first half to keep out efforts from Serge Gnabry, Sadio Mane, Benjamin Pavard and Leroy Sane.

Those missed chances almost came back to haunt Bayern when Ritsu Doan got an outstretched leg to Michael Gregoritsch's cross and sent the ball against the right-hand post. 

Bayern's breakthrough arrived through their first on-target attempt of the second half, with De Ligt's deflected shot from 25 yards swerving past a helpless Flekken.

Flekken produced one of the saves of the season soon after to deny Mane from close range, while Sane clipped the ball over the crossbar with just the goalkeeper to beat.

Sane squandered another chance when through one-on-one, but only after Yann Sommer had produced a superb save at the other end to keep out Roland Sallai's shot.

Gnabry struck the post in the closing seconds, while Matthias Ginter glanced wide from the final meaningful attack, but Bayern successfully saw out another crucial victory.

Bayern Munich head coach Thomas Tuchel urged his players to retain a positive mindset ahead of a crucial run of fixtures in the Bundesliga and Champions League.

Following a shock 2-1 defeat at home to Freiburg in the DFB-Pokal on Tuesday, Bayern travel to face the same opponents in the league on Saturday before going up against Manchester City in the first leg of their Champions League quarter-final next Tuesday.

Speaking at a press conference on Friday, Tuchel repeatedly mentioned a need to be "positive" despite the cup setback.

"We need to continue with a positive approach, we can be angry but still be positive," he said, later adding: "We need a reaction, but we would have needed one even if we won.

"People don't want to hear it but there were positive things in [the Freiburg] game... Things can happen where the result is probably not right after a game like this but we have to accept it.

"We are lacking a bit of precision in the last pass, a bit of trust, cohesion, creativity. We need form and that will only come back if we remain positive, even though we were unhappy with the result."

On the reaction of his players following the loss to a 95th-minute Lucas Holer penalty at the Allianz Arena, Tuchel added: "They are very critical of themselves. I was telling them the same thing I have told you, that we just have to accept it, that the coach is talking about positive things about the game even though no-one wants to talk about it.

"We can have a bad mood for a couple of days but that doesn't help anyone, you need a positive mindset to move forward."

Tuchel confirmed the Freiburg game will come too early for injured pair Eric Maxim Choupo-Moting and Mathys Tel, while Dayot Upamecano misses out through suspension.

When asked who can play as the striker in Choupo-Moting's absence, he said: "Mathys Tel can play as a nine, that was his answer when I asked him his position, but he is injured.

"Sadio Mane and Serge Gnabry can play there as well, they will be my players of choice."

The former Borussia Dortmund and Chelsea boss was not keen to look beyond Saturday to Tuesday's trip to Manchester, but he acknowledged he cannot use Freiburg as preparation given the difference in approach.

"I don't believe that we can practice the things we need against Man City, Freiburg play a completely different way," he said.

Manchester United, Bayern Munich and Barcelona have all reportedly met with the agent of 22-year-old Bayer Leverkusen right-back Jeremie Frimpong about a potential transfer.

Frimpong has exploded onto the scene this season as a weapon going forward, scoring eight league goals in 26 Bundesliga fixtures after just a single goal in his first 18 months in Germany.

Having previously represented the Netherlands at youth levels, his sparkling form was rewarded as he was included in their World Cup squad, although he did not get to make his senior debut.

He is viewed as one of Leverkusen's most valuable assets, and the club are expecting Champions League teams to come calling.

TOP STORY – UNITED LEAD THE CHARGE FOR GOAL-SCORING RIGHT-BACK

According to Sport Bild, United and boss Erik ten Hag have been in contact with Leverkusen "for weeks" trying to sort out the framework of a deal, with the German side reportedly starting the bidding at £44million (€50m).

The report states that asking price is not seen as a significant hurdle, and Leverkusen have already begun the process of replacing Frimpong with the signing of 20-year-old Brazilian Arthur from America MG in recent days.

Meanwhile, Fabrizio Romano adds Bayern and Barcelona have also had "direct meetings" with Frimpong's agent, although a decision on the future of Joao Cancelo remains the priority for Bayern, and Barcelona's finances make their situation unclear.

ROUND-UP

– Roma coach Jose Mourinho is in high demand, with Relevo reporting Chelsea have enquired about bringing him back for a third stint, while Corriere dello Sport claims he has received an offer from the Saudi Pro League that would pay him €120m over the next two seasons.

– Spanish publication COPE is reporting Chelsea, United and Tottenham are all investigating a potential move for 22-year-old Valencia goalkeeper Giorgi Mamardashvili, despite his gaudy £87m (€100m) release clause.

– According to Calciomercato, Newcastle United have been impressed with 21-year-old Feyenoord striker Santiago Gimenez, with the Mexican having starred in his first season in the Eredivisie.

– Inter are trying to fend off interest from Manchester City by signing 23-year-old centre-back Alessandro Bastoni to a new long-term contract, per Calciomercato.

Chelsea's dismissal of Graham Potter and decision not to rush into an appointment has generated speculation about their next permanent manager.

The Blues are destined to miss out on the Premier League's top four this season, thus will not qualify for the Champions League via the league.

As a result, there appears a lack of urgency as they look to get back on the right direction after sacking both Potter and Thomas Tuchel this term under new owner Todd Boehly.

TOP STORY – BLUES MULL OVER ENRIQUE, NAGELSMANN AND CONTE

Fabrizio Romano reports Frank Lampard will take over as Chelsea's interim manager, but that ex-Spain boss Luis Enrique is 100 per cent interested in the permanent position.

Enrique has flown into London for talks on the role, while the Blues will also continue talks with ex-Bayern Munich boss Julian Nagelsmann who is the leading candidate.

The Independent claims the Blues are also considering a shock return for Antonio Conte after initial contact between intermediaries.

ROUND-UP

– Football Insider reports Manchester United are keen on Southampton midfielder James Ward-Prowse. United may take advantage of the Saints' possible relegation to bolster their midfield with the 28-year-old free-kick specialist. Aston Villa and Newcastle United are also interested in him.

– Liverpool are willing to cough up €40 million (£35m) for Atletico Madrid's Argentinian World Cup winner Rodrigo De Paul to bolster their midfield next term, reports Fichajes. Inter Live claims Tottenham are also interested in De Paul.

– Arsenal are pondering an off-season move for Lazio midfielder Sergei Milinkovic-Savic who will be a free agent in 2024, claims Gazzetta dello Sport. The reported fee would be around €40m.

– Luka Modric is disgruntled with his contract situation at Real Madrid, with his future not yet resolved with only a few months left on his deal, claims Goal.

– Fichajes claims West Ham, Leeds United and Nice are all circling for Real Madrid's Mariano who will be available on a free transfer at the end of this season.

– Leicester City have shortlisted Ralph Hasenhuttl, Jesse Marsch and Oscar Garcia for their vacant managerial role according to Fabrizio Romano. The Independent's Miguel Delaney claims the Foxes are also interested in experienced pair Martin O'Neill and Rafa Benitez.

Bayern Munich sporting director Hasan Salihamidzic has outlined the club's plans to bring in a new striker in the transfer window after Tuesday's shock 2-1 DFB-Pokal defeat to Freiburg. 

Thomas Tuchel's side took the lead in their quarter-final fixture through Dayot Upamecano but were pegged back by Nicolas Hoefler's strike, before Lucas Hoeler's 95-minute penalty sent the Bundesliga leaders crashing out.

Bayern will now miss out on the final of the competition for the third successive season, and Salihamidzic was adamant signing a new striker will be necessary for the club to move forward next season.

"Of course we will sit down and see what we need to do in the transfer market," he said after the game.

"But the games show: To go into the new season with just Eric Maxim Choupo-Moting, Mathys Tel, Thomas Muller and Sadio Mane would be negligent.

"In all likelihood, there will be a new striker. Whether it's Harry Kane, Victor Osimhen or Randal Kolo Muani, the coming weeks will show."

Bayern remain top of the Bundesliga and are through to the quarter-finals of the Champions League, but they have struggled to replace the output of the talismanic Robert Lewandowski since his departure to Barcelona at the end of last season.

The Poland international scored 110 goals in just 94 league games in his last three seasons at Bayern as the club won three consecutive Bundesliga titles and the Champions League. 

Choupo-Moting has led the line in Lewandowski's absence this season but has scored just 10 league goals.

Despite the disappointing result against Freiburg, Salihamidzic remained positive about Tuchel's appointment and refused to lay the blame for the defeat at the door of the new boss.

"It is bitter for all of us, but it has nothing to do with the coach," Salihamidzic said.

"It's a process. He makes a very good impression and is doing a very good job. Today was bitter for all of us, but we will continue on Saturday."

Thomas Muller was left feeling bitter after Bayern Munich were saddled "with the shambles" of another DFB-Pokal failure against Freiburg.

The Bundesliga leaders slipped to a 2-1 defeat in the quarter-finals, after Lucas Holer's 95th-minute penalty condemned them to a late loss.

Dayot Upamecano had handed Bayern the lead in Thomas Tuchel's second game in charge, before Nicolas Hofler squared matters in the first half.

It means the club will miss out on the DFB-Pokal final for the third straight season, and Muller concurred the loss represented a blow to their pride.

"[There is] a certain bitterness," he told Sky Sport Germany. "We're eliminated. You can't make amends anymore. You're standing there with the shambles.

"It's over again. Of course that scratches your sense of honour. Freiburg hardly had a chance to score, but if you lose in the end, you have to face the questions."

The result means it is one win and one loss for Tuchel since he succeeded Julian Nagelsmann, having picked up a 4-2 win over Borussia Dortmund in his first game.

Muller appreciated the need to adapt to their new coach, but still stressed the blow of their exit would linger, particularly with a rematch in the Bundesliga on Saturday.

"We [have] now had two games with a new coaching line-up," he added. "Now, we're emotionally down to earth. We have to manage that as a group.

"We will get back together on Thursday, we will try to improve. But now, there is disillusionment and brutal disappointment."

Thomas Tuchel accepted responsibility for Bayern Munich's DFB-Pokal quarter-final exit, after they suffered a late 2-1 loss against Freiburg.

The Bundesliga leaders looked set for extra-time at Allianz Arena, after Dayot Upamecano's header was cancelled out by Nicolas Hofler.

But Jamal Muisala's penalty concession deep into second-half stoppage time allowed Lucas Holer to seal a last-gasp victory for the visitors from the spot.

In only his second game in charge since replacing Julian Nagelsmann, Tuchel acknowledged he had to shoulder the blame for their defeat.

"I am not really angry," he said. "We conceded two goals with two shots. I can’t remember another chance from Freiburg.

"The last pass, [and the] precision obviously, are all an issue. But still, we had good moments we could have used, but [we] just could not keep it up.

"In the end, it is our fault. We are very disappointed [to lose] a quarter-final at home. Of course, I am responsible."

Tuchel made a winning start to his Bayern career with a decisive 4-2 win over old club Borussia Dortmund, where he previously won the DFB-Pokal.

His failure to back it up with progress to the semi-finals of Germany's major knockout competition will take the shine off his early impression.

Bayern can claim immediate revenge on Saturday when they travel to Freiburg for a reverse fixture in the Bundesliga, looking to consolidate top spot.

They also remain in the mix for Champions League honours, and return to European competition against Manchester City next Tuesday.

Lucas Holer's last-gasp penalty saw Freiburg snatch a dramatic 2-1 victory against Bayern Munich in the DFB-Pokal quarter-finals to end Thomas Tuchel's hopes of a domestic double.

The tie appeared to be headed to extra time, until Jamal Musiala handled Nicolas Hofler's strike, enabling Holer to secure a shock win.

Bayern had looked the likelier of the two teams to claim a late winner, after seeing Dayot Upamecano's first-half header cancelled out by Hofler's excellent volley.

It means Tuchel, in his second game since replacing Julian Nagelsmann, will miss out of the chance of both Bundesliga and Pokal glory as Christian Streich's side proceed to the last four.

Lionel Messi appeared set to re-sign with Paris Saint-Germain late last year, but the situation has changed.

There have been reports that the Argentinian World Cup winner is unhappy at PSG, with links to an MLS move.

Messi is contracted until the end of this season and had initially agreed to a one-year extension to stay in the French capital.

TOP STORY – MESSI AND PSG RELATIONSHIP IRREPARABLE

L'Equipe claims Messi's relationship with PSG irreparable and he is all but certain to exit at the end of this season, with a return to Barcelona appearing increasingly likely.

Messi spent more than 20 years at Camp Nou, before Barca's financial challenges led to his departure for PSG in August 2021, with the club keen to welcome him back.

The 35-year-old was jeered by PSG fans during Sunday's 1-0 home loss to Lyon amid speculation of his departure.

ROUND-UP

– The Athletic reports signing Tottenham forward Harry Kane is Manchester United manager Erik ten Hag's "absolute priority" in the off-season. Kane is out of contract with Spurs in 2024.

– The Sun claims United are strongly considering selling under-performing winger Jadon Sancho in the off-season, with a view to using the sum generated to purchase their next forward.

– United have also held exploratory talks with Bayern Munich defender Benjamin Pavard, per The Athletic.

– Real Madrid have been linked with Chelsea's Reece James and Football Insider claims they are willing to pay £90m (£102.5m) for his services, with 31-year-old right-back Dani Carvajal struggling with injuries.

– Arsenal are plotting a move for Aston Villa striker Ollie Watkins during the next transfer window, according to Fichajes.

– Talksport claims  Graham Potter has declined the opportunity to become Leicester City 's new manager, with The Mail reporting that he will wait until the off-season before taking on a new role.

Chelsea sacked Graham Potter on Sunday after barely seven months as their manager.

Potter, who took over from Thomas Tuchel in September, led the Blues to 12 wins, eight draws and 11 defeats.

His demise comes amid numerous changes of managers at Premier League clubs, with Tottenham last week parting with Antonio Conte.

TOP STORY – CHELSEA APPROACH TOP CANDIDATE NAGELSMANN

Chelsea have identified ex-Bayern Munich head coach Julian Nagelsmann as their top candidate and approached him already, claims Fabrizio Romano.

Romano said talks will be ongoing before a final decision, while he added the Blues hierarchy are admirers of Sporting boss Ruben Amorim.

However, Sky Sports Germany claims Nagelsmann is not interested in taking over at Chelsea.

TalkSPORT claims the dismissed Potter could be offered an immediate return to management by Leicester City who sacked Brendan Rodgers earlier on Sunday.

ROUND-UP

– AS claims that Paris Saint-Germain winger Kylian Mbappe has told the Real Madrid board that he intends to join Los Blancos as a free agent in 2024. According to the report, Madrid are not willing to negotiate a transfer fee with PSG, following their long-running interest in Mbappe, with the player needing to get out of his contract to move to the Spanish capital.

– Liverpool will consider an off-season move for Chelsea midfielder Conor Gallagher, reports The Independent.

– Fichajes claims Liverpool are also weighing up a surprise move for Real Madrid midfielder Eduardo Camavinga.

– Football Insider claims Arsenal have identified three midfield targets in Everton's Amadou Onana, West Ham's Declan Rice and Brighton and Hove Albion's Moises Caicedo.

– Manchester United's hopes of signing Eintracht Frankfurt forward Randal Kolo Muani have been set back with the Frenchman keen to join Bayern Munich in the off-season.

Borussia Dortmund hoped there had been a sign of change. BVB were back on top of the Bundesliga ahead of Der Klassiker and going to rivals Bayern Munich as the league's in-form team, their hosts meanwhile were in self-inflicted turmoil.

Victory at Allianz Arena would be the real statement Dortmund desired in a quest to prove they could end Bayern's domination of not only German football's biggest game, but the Bundesliga in general.

And perhaps Dortmund will still go on to win the title, but Saturday's match suggested that no matter how good BVB are, Bayern's psychological hold over them will take years to overcome.

As Bayern cruised to a 4-2 win, the Bundesliga's title race took another turn.

There had been plenty of talk about confidence from the Dortmund camp coming into the game, with CEO Hans-Joachim Watzke managing to perfectly encapsulate Bayern's recent dominance of this fixture when saying they were travelling "to Munich with a lot of self-belief for the first time in a long time".

He was referring to the fact BVB hadn't won at Allianz Arena in the Bundesliga since 2014, when Jurgen Klopp was still in charge, and their run of eight – now nine – successive league losses away to Bayern was their second-worst streak against any club in their top-flight history.

They'd been on the end of some hammerings in that time, too, losing by three or more goals five times.

So, when Dortmund began with genuine promise and swagger on Saturday, there was at least a suggestion Bayern weren't going to have it all their own way.

Dortmund were aggressive in their pressing and incisive with their distribution. Marius Wolf's energy down the right looked a potential weapon; Jude Bellingham showed some classy touches; Marco Reus' off-the-ball runs caused Bayern issues.

In fact, had Reus got his shot off a fraction of a second earlier in the seventh minute after Wolf's clever release, he may well have given BVB an early lead – as it was, Matthijs de Ligt got across to make a vital block.

But as predictable as some might have suggested a comfortable Bayern win was, there was nothing inevitable about the moment everything changed on Saturday.

Dayot Upamecano's pass from just inside his own half was seemingly routine for Gregor Kobel, but the goalkeeper took his eye off the ball as he raced out to clear, getting a slight nick on the ball to score arguably the most remarkable own goal of the season.

It's impossible to definitively say if things would've been different without that horror show, but Dortmund ceased to be much of a threat from that point in the 13th minute.

The following 10 minutes saw Bayern build a handsome lead. Thomas Muller was on hand to nudge home from De Ligt's headed flick-on to make it 2-0, and then punished another Kobel mistake with a tap-in when Leroy Sane's long-range strike was only parried.

It was effectively game over inside a quarter of the contest. Dortmund may have been the Bundesliga's form team coming into the weekend, but their first-half collapse had them reverting to type in Der Klassiker.

It wasn't over yet either.

Bayern looked especially potent in the opening half when attacking from the flanks, with Sane and – in particular – Kingsley Coman absolutely devastating at times.

Their deployment as inverted wingers was one of few significant alterations to the Bayern setup from Tuchel. It worked a treat almost throughout, and its success was tangible with the fourth goal early in the second half.

Sane cut in from the right, played a perfectly weighted pass towards the back post – through the legs of Muller – and Coman was there to stab home.

No one would have expected wholesale changes from Tuchel. After all, he's only had a couple of days to work with much of the squad following the international window.

But such a subtle yet demonstrably effective tweak perhaps highlights why Bayern were so keen to not miss out on the opportunity to finally hire Tuchel.

Similarly, Bayern were thrilling to watch, and we know just how important that is.

"We've come to the conclusion that the quality in our squad – despite the Bundesliga title last year – has come to the fore less and less often. After the World Cup we have played less successfully and less attractively. The big fluctuations in performance have cast doubt on our goals for this season, but also our goals for the future. That is why we have acted now."

Club CEO Oliver Kahn's comments after Julian Nagelsmann's sacking were pretty brutal but offered a lot of clarity to not only the man he'd just fired, but also the one he'd just hired.

Dortmund's late consolations via an Emre Can penalty and Donyell Malen's precise finish might be indicative of some of the issues with Bayern's mentality towards the end of Nagelsmann's reign. The 5-3 win over Augsburg comes to mind.

But 4-2 was a scoreline that flattered Dortmund. If anything, Bayern were a little wasteful, and had they checked their runs better, more goals certainly would've arrived.  

In some ways, this win was almost as close to the perfect start as Tuchel could have enjoyed when you consider the reservations Bayern started to have with Nagelsmann.

It will have likely dealt Dortmund a psychological blow, while Bayern find themselves back at the top of the table having produced an entertaining attacking spectacle.

But this wasn't where the title was won and lost – Bayern's shaky post-World Cup form proves Tuchel still has a lot of work to do.

Arsenal, Manchester United and Paris Saint-Germain are among the heavy hitters with reported interest in out-of-favour Real Madrid midfielder Aurelien Tchouameni.

Tchouameni arrived in Madrid last July from Monaco for a €100million fee, but has started just 15 of 26 LaLiga fixtures this term, and played only a combined six minutes in their two-legged Champions League clash with Liverpool, whom he reportedly turned down to move to the Santiago Bernabeu.

The defensive midfielder has found himself behind 20-year-old Eduardo Camavinga for Madrid's most crucial contests, also only making brief substitute appearances in both meetings with Barcelona in March.

Tchouameni, who has made 23 senior appearances and scored two international goals for France, still has plenty of time to turn himself into the impact player Madrid envisioned, but the club are reportedly weighing up if they could cash in and use the resources elsewhere.

TOP STORY – EUROPE'S ELITE KEEP A CLOSE EYE ON TCHOUAMENI

According to El Nacional, Madrid are not happy with such an expensive signing only being used sparingly in a rotation role, and will consider any bid in the next transfer window starting at €70m (£61.5m).

The report names Arsenal, United, Paris Saint-Germain, Liverpool and Chelsea as Tchouameni's "admirers", with the Premier League clubs in particular having all been in the market recently for help in central midfield.

Tchouameni could even cost less than breakout Brighton and Hove Albion star Moises Caicedo, and significantly less than Borussia Dortmund talent Jude Bellingham, adding another key name into the mix for midfielder-hungry clubs this offseason.

ROUND-UP

– According to Calciomercato, Liverpool are considering a move for Brighton's Caicedo if their pursuit of Bellingham is unsuccessful.

– Football Insider is reporting that Chelsea are hoping to receive £100m in return for midfield duo Mason Mount and Mateo Kovacic in an effort to balance the books after lavish spending.

– Chelsea's Kai Havertz has interest in reuniting with former boss Thomas Tuchel at Bayern Munich, and that interest is mutual according to 90min.

– Fichajes is reporting that Roma may swoop for 32-year-old United goalkeeper David de Gea if he does not sign a new contract to stay in the Premier League.

– According to Mundo Deportivo, PSG have told Lionel Messi they will pay whatever is necessary to retain his services amid heavy interest from Barcelona and Inter Miami.

Real Madrid need a transition plan as captain Karim Benzema heads towards his late thirties, and that could lead them to making a summer swoop for a new forward.

There has been plenty of speculation about Mohamed Salah's future with Liverpool over the past few months, even with the 30-year-old Egyptian being contracted to the Reds until 2025.

Rumours have continued to emerge about a possible move, but Madrid also reportedly have their eye on Victor Osimhen, Harry Kane and Rasmus Hojlund as they consider various options.

TOP STORY – REAL MADRID WANT A NEW STRIKER

Real Madrid might see Liverpool forward Mohamed Salah as an option for an off-season transfer, claims Defensa Central.

The report claims Los Blancos could consider Salah while they also look at other possible acquisitions, including Napoli's Serie A top scorer Victor Osimhen and Tottenham's ever-prolific Harry Kane.

Karim Benzema turns 36 later this year, and Madrid will need other proven frontline options for when the Frenchman steps away from the spotlight.

Rasmus Hojlund, who has settled in well at Atalanta this season, is also said to be admired at Madrid, no doubt helped by him scoring five goals in his first two starts for Denmark during the recent international break.

ROUND-UP

– The Guardian claims Mason Mount is open to a move to German champions Bayern Munich amid swirling rumours about their new boss Thomas Tuchel's interest in a reunion. Mount and Chelsea have reportedly reached a stalemate in their discussions on a new contract. Tuchel left Chelsea in September.

– Manchester City have identified Borussia Dortmund's Youssoufa Moukoko as a target, reports Football Transfers. The report claims City are fearing Erling Haaland's exit but could use any incoming funds to facilitate a move for the Dortmund forward.

– David de Gea has rejected Manchester United's initial new contract offer which he believes is not adequate, according to The Athletic. The 32-year-old Spanish goalkeeper is out of contract at the end of this season, with United proposing a pay cut in his new deal. The report states an agreement on new terms is expected to be reached.

– Bayern are not interested in either of West Ham's Declan Rice or Chelsea's Mateo Kovacic, reports Sky Sport Germany's Florian Plettenberg.

With the last international window of the season over, domestic club campaigns now enter the final straight.

Everything is still to be decided – technically speaking. Title races, European qualification, relegation – all will come to a head over the next two months.

Of course, there are a few outcomes that already look like foregone conclusions, but there's still much to play for in each of the top five leagues.

With club football returning over the next few days, Stats Perform's Artificial Intelligence team have crunched the numbers using their supercomputer to predict the outcome of each league.

How's the outlook for your team?

Premier League

England is the scene of potentially most compelling title race among the top five leagues this season.

Arsenal may have an eight-point lead at the summit, but Manchester City still have a game in hand. As such, the Gunners' chances of winning a first league title since 2004 are 56.2 per cent, perhaps smaller than many might have expected.

That comes down in part to the statistical value attached to City's historic results, particularly over the past few years during their Premier League domination, whereas Arsenal haven't come close to that level of success over the same period.

Therefore, the title race still looks tight.

A little further back, Manchester United (74.5 per cent) are near-certainties to finish third, while the race for fourth promises to be engrossing – Tottenham (19.3 per cent), Newcastle United (29.1 per cent) and Liverpool (24.5 per cent) look set to tussle it out, with Brighton and Hove Albion (10.7 per cent) considered rank outsiders.

At the bottom, Southampton's 41.6 per cent likelihood of finishing 20th suggests they've a huge battle on their hands, but the supercomputer reckons West Ham and Leicester City have enough to pull themselves clear of the drop zone.

The signs are that two of Bournemouth, Everton and Nottingham Forest will join Saints in the Championship.

Bundesliga

Germany's top flight may come to rival the Premier League's title race. Ahead of the weekend's Klassiker between Borussia Dortmund and Bayern Munich, BVB are a point clear.

Yet, Dortmund's probability of finishing top is just 22.4 per cent compared to Bayern's 76.4. Again, it largely comes down to their historic results and Die Roten's dominance suggesting they'll eventually get the job done.

But it's fair to say Bayern's decision makers aren't so confident given their brutal choice to sack Julian Nagelsmann on Friday, replacing him with former Dortmund coach Thomas Tuchel.

Union Berlin aren't out of it given they are only five points behind Dortmund, though this is obviously uncharted territory for them, hence the 0.9 per cent chance of winning their first top-flight title since 1923.

Third looks the best bet for them (40.3 per cent), while RB Leipzig are the most likely to fill out the top four (37.2 per cent).

It's even tighter in the relegation scrap. Only seven points separate 18th from 13th, so even rock-bottom Stuttgart are given a reasonable chance of finishing 14th (10.6 per cent) or 15th (15.2 per cent).

LaLiga

Following Barcelona's dramatic 2-1 win in El Clasico before the international break, LaLiga looks done and dusted at the top with the Blaugrana 12 points clear.

The supercomputer also reckons Atletico Madrid are nearly guaranteed third (80.3 per cent), leaving what is effectively a two-horse race for fourth.

Real Sociedad have fourth at the moment and are 43.7 per cent likely to finish there, though Real Betis (36.7 per cent) aim to push them all the way.

At the other end, Elche are given no more than a 0.1 per cent chance of getting out of the bottom three after taking just 13 points from 26 games.

Otherwise, relegation is difficult to call. Almeria in 19th are only six points behind Real Mallorca in 11th, meaning there are a host of clubs who could yet get dragged into a fight for their lives.

There are two particularly big names among those potentially in trouble. Valencia are in the bottom three and have a 21.9 per cent chance of being relegated, while Sevilla – who are on their third coach of the season after sacking Jorge Sampaoli – are only two points clear of safety.

The computer says Man Utd's next Europa League opponents only have a 5.8 per cent probability of going down, however.

Ligue 1

Paris Saint-Germain seemingly have little to worry about in Ligue 1, with the supercomputer calculating their title chances at 98 per cent.

The tiny hint of doubt gives Marseille (1.8 per cent) and Lens (0.2 per cent) a bit of hope – but even then, it's presumably nothing more than a pipe dream.

There is a similar degree of certainty at the bottom, where four teams will be relegated ahead of the league's size being reduced to 18 clubs next term.

Angers, with 10 points from 28 games, cannot get out of the bottom four according to the calculations, and the other three positions are currently taken up by Ajaccio, Troyes and Auxerre.

Brest and Strasbourg aren't out of the woods yet either, though the supercomputer believes those in the relegation zone are the ones most likely to drop into Ligue 2.

Serie A

If there's one league in Europe that's got a foregone conclusion at the top, it's Serie A.

Napoli have more than a 99.9 per cent chance of winning a first Scudetto since 1990, with the unrelenting Partenopei a whopping 19 points clear of second already.

The race for Champions League qualification promises to be a little more tense.

Eleven points is the gap between Lazio in second and Juventus in seventh. While the Bianconeri are very much outsiders, the other five teams have at least a 15 per cent chance of finishing in the top four.

Lazio, Inter and Milan appear to be the most likely to take those spots, though Roma and Atalanta will fancy their chances of putting a cat among the pigeons.

In the relegation fight, there's a rather clearer picture.

Cremonese and Sampdoria look doomed, while Hellas Verona in 18th are five points adrift of safety, giving them just an 18.8 per cent probability of avoiding relegation.

Bayern Munich will always be favourites to beat Borussia Dortmund, with Leon Goretzka suggesting no team can face Die Roten at Allianz Arena and have the upper hand.

The two teams meet in their first game back from the international break in what could be the most decisive encounter of the Bundesliga title race this season.

Dortmund hold a one-point lead over their rivals, who dismissed coach Julian Nagelsmann and replaced him with former Black and Yellow boss Thomas Tuchel last week.

Speaking ahead of the crunch clash though, Goretzka insisted the visitors' advantage in the league table means nothing when they go to Allianz Arena, given the hosts' pedigree.

"We are ready," he told SportBILD. "We want the 11th championship in a row. To quote Kylian Mbappe, we are always favourites.

"When we play at home, there isn't a team we don't go into the game against as favourites. I think [the pressure] is great.

"I really enjoy these games. As a player, you don't want to be part of the team that can break this series [and miss out on another title win]."

Nagelsmann's departure, despite guiding Bayern to the title last term and the Champions League quarter-finals this year, is a gamble for the Bavarian giants.

But in Tuchel, they have a former Champions League-winning coach from his time at Chelsea, and Goretzka hopes he can help retain their Bundesliga crown.

"We all know and appreciate his successes," he added. "[We] have great respect for his achievements and experience."