Rafael Nadal and Nick Kyrgios could face off in the inaugural United Cup, while WTA world number one Iga Swiatek will represent Poland.
The United Cup is the new warm-up tournament for the ATP and WTA Tour seasons, and will take place in Australia in December and January.
While ATP world number one Carlos Alcaraz will not feature, compatriot Nadal will be competing for Spain, and they have been drawn alongside Australia and Great Britain in Group D.
Those matches will be played in Perth, with a clash between Nadal and Kyrgios, who have enjoyed an entertaining rivalry down the years, in the offing.
They were set to meet in the semi-finals at Wimbledon this year, but Nadal withdrew due to injury, handing Kyrgios a walkover into his first grand slam final, which he lost to Novak Djokovic, who will not be playing in Australia.
Serbia are not among the batch of teams taking part, but even so, there remains doubt whether Djokovic would be able to enter Australia given his stance against the COVID-19 vaccine, which eventually saw him deported from the country after a drawn-out legal battle ahead of this year's Australian Open.
Emma Raducanu has decided against playing for the British team, which also does not feature Andy Murray.
Casper Ruud, the beaten US Open finalist, will play for Norway in Group E, in Brisbane, while Alexander Zverev will be in action for Germany.
Swiatek is the biggest name from the WTA Tour to enter, with the brilliant 21-year-old lining up alongside Hubert Hurkacz for Poland in Group B.
Maria Sakkari and Stefanos Tsitsipas, along with his brother Petros, will team up for Greece in Group A.
Two more countries will be admitted to the tournament later in November.
Alcaraz begins Madrid Open campaign with emphatic win
Carlos Alcaraz continued his fine record at the Madrid Open with an emphatic 6-2 6-1 victory over Alexander Shevchenko on Friday.
The two-time defending champion made it 12 straight wins at his home tournament to ensure he will face Brazilian Thiago Seyboth Wild in the last 32.
Alcaraz was playing his first match on the ATP Tour since March 28 after being unable to compete in the Monte-Carlo Masters and Barcelona Open due to an arm injury.
But he was still able to make a fine start to his clay-court season, breaking serve in the first game and racing to victory in only one hour and eight minutes.
Data Debrief
Sometimes the scoreline can be harsh on a beaten player, but on this occasion Alcaraz was clearly dominant, breaking the Kazakh seven times in the match and forcing 11 break-point opportunities while conceding only three for his opponent.
That allowed the Spaniard to claim a dominant victory despite being broken once in each set. He will now turn his attention to a clash with Seyboth Wild, who battled past Lorenzo Musetti with a 6-4 6-4 win.
Reigning champion Sabalenka pushed by Linette at Madrid Open
Aryna Sabalenka got her Madrid Open campaign started with a 6-4 3-6 6-3 win over Magda Linette on Friday.
Sabalenka could not quite hit her peak form against Linette, but the world number two nevertheless got the job done after going the distance.
The Belarusian is hunting a record-equalling third title in Madrid, where she is the reigning champion, though she has not won back-to-back matches at a tournament since winning the Australian Open.
"It's not about being confident," Sabalenka said. "It's about how much you're ready to do to get it. It's about the hard work and to be ready, be ready for the big fights. I feel like confidence is not going to help you in those big matches. It's about staying there and fighting for it."
Data Debrief
Sabalenka (70 per cent, 56-24) is now one of five active players since 2020 to hold a winning percentage of 70 per cent or higher at WTA-1000 events.
Iga Swiatek, Simona Halep, Elena Rybakina and Jessica Pegula are the other players to feature on that list.
Rybakina continues clay winning streak with victory over Bronzetti
In-form Elena Rybakina has moved into the last 32 of the Madrid Open after a straight sets victory over Italian Lucia Bronzetti.
Number four seed Rybakina triumphed 6-4 6-3 on Friday and will next face either Marta Kostyuk or Mayar Sherif.
Rybakina was broken early in each set but ultimately had few problems getting over the line, converting four of her five break points to continue an impressive run of results after winning the Stuttgart Open last week.
She has now won five consecutive WTA matches and has 13 straight wins on clay courts to her name in a superb streak that started one year ago.
Data Debrief: Rybakina in elite company
Since the start of 2020, only two other players have claimed as many 13 consecutive WTA wins on clay, and they are Iga Swiatek and Simona Halep, so Rybakina is in elite company.
Rybakina's last defeat on this surface came in the 2023 edition of the Madrid Open, when she fell to Anna Kalinskaya in her first match, so this win represented a better start to her campaign in the Spanish capital.
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