The president of the French Football Federation has claimed that managerial target Zinedine Zidane could instead take the job at Paris Saint-Germain.
The 49-year-old has been out of the game since leaving Real Madrid for a second time at the end of last season but has not been short of offers over the past several months.
Manchester United were at one point linked with Zidane's services, but the Red Devils instead elected to bring Erik ten Hag to the club for the 2022-23 season.
PSG boss Mauricio Pochettino is still in limbo over his own future, though, with the Argentine easing to the Ligue 1 title with Les Parisiens but suffering a last-16 Champions League collapse at the hands of Real Madrid.
Zidane is thought to be PSG's favourite to take over if Pochettino makes an expected departure from the Parc des Princes, but the Frenchman is understood to have been holding out for the Bleus job.
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Didier Deschamps's France contract is due to expire after the World Cup in Qatar, but FFF president Noel Le Graet has claimed that PSG is a likely destination for Zidane.
"You have to be careful what you say. Zidane has shown Madrid that he has qualities that were barely imaginable," the FFF chief told L'Equipe when questioned on the possibility of Zidane taking the France job.
"In the minds of the French, he may be a successor. But that's not my goal. We'll see. If Didier and I go our separate ways, he will surely be one of the options.
"Do you see me saying today: 'Is it Zidane who will replace Deschamps?' We'll see. Zidane might take on PSG. For the France team, you have to be free. But today, we are going to do everything to put Didier in the best conditions to win this World Cup.
"We want to defend our title. But the objective is at least the last four, as usual. Will Deschamps be kept if this objective is not fulfilled? We'll discuss that later. He is our employee, but he's also a friend. I have a very courteous relationship with him."
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Zidane's two spells at Real Madrid saw him establish a reputation as one of the world's leading managers, winning three consecutive Champions Leagues as well as two La Liga titles, two Copa del Reys, two Spanish Super Cups, two UEFA Super Cups and the Club World Cup twice.
Zidane was also named the World's Best Club Coach in 2017 and 2018 following his European successes, and he took charge of 263 games for Real Madrid during his two spells at the club.
The 1998 Ballon d'Or winner posted 174 wins, 53 draws and 36 losses at the Bernabeu helm and set numerous records as Real Madrid manager, including a 40-game unbeaten run - the longest ever in Spanish football.
Zidane is also one of three men to have won three Champions League titles as a manager alongside Bob Paisley and Carlo Ancelotti, but the latter will be out to make it four in this year's final against Liverpool.
Tottenham Hotspur manager Antonio Conte was also a rumoured target for PSG to replace Pochettino, but the Italian proceeded to blast such links as "fake news".