Mbappe will be a free agent next summer and will be able to sign for his future club on Jan. 1.
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“We hope that on Jan. 1 everything can be resolved,” Perez said on Tuesday when asked about Mbappe’s future.
However, Perez clarified his comments soon after in the French media, saying: “My words were misinterpreted. What I said is that we have to wait until next year… always with respect to PSG with whom we have good relations.”
A long-term target of Madrid, Mbappe, 22, opened up on his future on Monday and confirmed he informed PSG of his intention to leave the club in July.
“I wanted the club to receive a transfer fee to bring in a quality replacement,” Mbappe told RMC. “I said it early enough so that the club could react.
“I wanted everyone to come out of this stronger, that we leave hand in hand, to make a good deal, and I respected that. I said, if you don’t want me to leave, I will stay.”
The World Cup winner also told L’Equipe on Tuesday that he would only leave PSG to join Madrid and hinted doubts remain around his future in France.
PSG rejected a €200m offer from Madrid on transfer deadline day despite Mbappe having made it clear he did not wish to renew his contract with the French giants.
Madrid were in a position to make that bid despite being hit by the coronavirus pandemic after careful financial management.
“Madrid have sold players for €200m,” LaLiga president Javier Tebas said last month. “They have money to sign both Mbappe and [Erling] Haaland. They have not lost money. On top of that, they have sold assets.”
Madrid’s interest on Mbappe goes back to 2012 when he had a trial at the club on his 14th birthday.
The Spanish giants wanted to sign Mbappe after he left AS Monaco in 2017 but he chose to join PSG in a €180m deal, which still stands as a world record fee for a teenager.
The France international has won three league titles during his four years in Paris and finished as Ligue 1’s top scorer for three seasons in a row.
Mbappe has scored four goals and set up five more in 11 appearances in all competitions for PSG this season.