"Hopefully it will be at Paris Saint-Germain, it would be with a great pleasure".
The French worldwide suggested it could be time to take on more responsibility in comments which will alert Europe's biggest clubs.
Should he decide to leave the French champions, Mbappe will have his choice of each of the world's elite football clubs.
"Strong links have united PSG and Kylian Mbappe for two years and that same story will continue next season", PSG wrote in a statement published on social media.
"We have the same ambition, we want to make history in European football, especially on the 50th birthday of PSG".
"Each major actor will play their part with the emphasis always on the collective.".
Reports have suggested that PSG, should they have opted to sell, could command as much as €300 million for the World Cup victor - a fee that would end the club's Financial Fair Play worries.
The source added that Mbappe's intentions on Sunday were never to push for a move, at least not this summer, but instead to put PSG under pressure.
Mbappe believes he's the best player on the club and wants to be regarded in that way.
Mbappe, who starred as France won the World Cup in France past year, has also secured Coupe de France and Coupe de la Ligue glory with PSG.
The 20-year-old backed up his excellent 2018 World Cup, where he scored four times as France won the trophy, by netting 38 times for PSG this season.
It is clear that PSG will try to do everything possible to retain Neymar and Mbappe, so the man sacrificed will be Cavani in order to comply with FFP regulations. "The moment of having more responsibilities, maybe at PSG, maybe elsewhere", he told BeIN Sports.