Report: Mbappe agrees to personal terms with Real Madrid
However, PSG are reportedly trying to convince Mbappe to change his mind and extend his stay in the French capital.
The 23-year-old, whose contract with PSG expires June 30, said Sunday he was "almost" ready to make a decision about his future and that he'd make an announcement before France's Nations League game against Denmark on June 3.
"My story goes on. I keep on winning, I'm never satisfied, and that's good," Mbappe said after being named Ligue 1's player of the season for a third consecutive year.
PSG seemed confident in January they would agree to a short-term contract with the World Cup winner, avoiding the embarrassment of losing one of the best players in the world on a free transfer. Mbappe refused to make any definitive statements during the season and remained tight-lipped when PSG drew Madrid in the Champions League round of 16. Mbappe scored twice against Los Blancos, but PSG lost 3-2 on aggregate.
Madrid now appear to have won Mbappe's signature after reportedly offering €160 million for the player last summer.
PSG director Leonardo criticized Madrid's behavior in October, saying they showed a lack of respect and must face punishment for openly courting the high-scoring forward over the last two years.
"We've never planned PSG's future without Mbappe," Leonardo added.
Mbappe has 169 goals and 79 assists in 246 appearances across all competitions since joining PSG from AS Monaco in 2017 for an eventual €180 million.