Mbappe is the hottest prospect on the planet and is expected to enjoy a stellar career at the top level of the game.
The 19-year-old has already won four trophies at club level, as well as the World Cup with France in July.
Mbappe’s performances have drawn admiring glances from across the globe with plenty of elite clubs said to be keen on him.
Barcelona, Real Madrid and Manchester City are among the teams credited with interest in snapping the forward up.
Desailly, who won the World Cup with France in 1998, has now predicted his countryman will leave PSG one day.
But he says Mbappe and team-mate Neymar are content with life at the Parc des Princes for now.
“[PSG] still have the challenge of the Champions League, which is really the key target,” Desailly told beIN SPORTS.
“[PSG spending money] helps the French football also to grow.
“Lyon have tried to invest.
“Monaco have dropped a little bit but we hope they come and they will invest.
“Bordeaux is abut to be sold, then bring some energy into the system.
“Marseille obviously have big potential, a chairman who can invest again and try and compete against PSG.
“So Ligue 1 is still very attractive and I do believe that those players are happy to be there.
“Mbappe, for sure, is not going to finish his career in Paris Saint-Germain.
“But for him it is an amazing transition so he will stay a couple of years.
“You’ve seen Neymar, Paris give him the tools to potentially become the best player of his generation.
“I see Paris Saint-Germain in good shape for the future.”
Mbappe has already bagged 15 goals in 14 games for PSG so far this season.
And he will be desperate to get back on the scoresheet against Marseille on Sunday night.
PSG already boast an eight-point lead over second-place Lille having won all ten of their Ligue 1 matches this term.