The 20-year-old, who has been linked with a move to Real Madrid, shocked Les Parisiens last month when he claimed his future could lie elsewhere.
And Spanish TV channel El Chiringuito has reported the World Cup-winning striker has requested to leave the Ligue 1 champions.
Real Madrid boss Zinedine Zidane is eyeing a massive squad overhaul this summer and Los Blancos have been linked to Mbappe’s PSG team-mate Neymar too.
PSG manager Thomas Tuchel recently admitted that he couldn’t guarantee either player staying in Paris beyond the summer.
He told reporters: “As a coach, I do want them to continue, but this is football, we are not naive.
“Many clubs want to transfer many players and the market is crazy, but if you ask me, the coach, yes, I want them here next season.
“But if they are not, we will find solutions.”
On his future after being named as the Ligue 1 Player of the Year, Mbappe said: “It’s a very important moment for me, I come to a turning point in my career.
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“I have discovered a lot here, and I feel it is perhaps the moment to have more responsibility.
“I hope that can maybe be at Paris Saint-Germain, that would be a great pleasure, or perhaps elsewhere with a new project.”
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Real could have a new front line next season if they get Mbappe after announcing the signing of Luka Jovic from Eintracht Frankfurt on a six-year deal.