The skillful striker has been linked with a move to Liverpool in recent months after apparently deciding not to renew his contract at Parc des Princes.
He could get a transfer to the Premier League once his deal expires in June 2022, although Real Madrid might have something to say about it.
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Le Graet reacted to transfer rumors by saying “you better stay” with PSG.
He told a French source The Parisian (Going through But): “I want him to stay in France, and at PSG. He is young and PSG still have many challenges to overcome.
“It doesn’t concern me directly, but players at this level, I prefer them to be with us.
“My preference is very clear, and in my opinion it’s even better to stay. “
Mbappe had another breathtaking campaign in 2020/21, recording 27 goals in just 31 Ligue 1 appearances.
He has also scored eight in 10 Champions League games. However, PSG’s season has been a disappointment in its own high standards as they were beaten to the league title by Lille.
They were also beaten in the Champions League in the last four by Manchester City by Pep Guardiola.
Mbappe was named to the bench for the 2-0 second leg loss after suffering an injury. If he had played, the contest could have gone very differently.
Mbappe has scored 132 impressive goals in 171 games for the French giants since arriving from Monaco in July 2018.
He has already reimbursed pretty much all of the £ 130million expenses they paid for him, although his ultimate goal is to bring the Champions League trophy back to France.
The 22-year-old has been asked about his future after winning the Ligue 1 Player of the Season title.
He said: “What I want is to win, and for there to be a solid project around me. It is the most important. I eat and live football and the sports project is very important.
“We will talk to the club and see what happens. Anyway, I’ve always been happy here. I understand that everyone is waiting for my answer. We will do things in order.