Leonardo, the former Brazil international who heads up the sporting division at PSG, said he has no reason to believe the superstar forwards will be departing in the next transfer window.
"Nothing tells us [that they won't be staying]," Leonardo said.
"They still have two years on their contracts, and we're thinking mainly about what comes after that with them. We want to move forward."
Speaking to Le Journal du Dimanche, Leonardo highlighted French World Cup winner Mbappe's value to the club.
The 21-year-old former Monaco player has been linked with clubs including Real Madrid and Liverpool, but barring a dramatic change in circumstances there seems little prospect of PSG allowing him to leave the Parc des Princes.
"He is the future of PSG. That is what everyone wants," Leonardo said.
Both Neymar and Mbappe are under contract until the end of the 2021-22 season.
Particularly in Mbappe's case, PSG will want to secure a long-term extension.
"The ideal would be to extend [his contract]," said Leonardo. "Among the top five players in the world, Lionel Messi and Cristiano Ronaldo are 32 and 35 years old; Neymar and Mbappe are 28 and 21 years old and they are with us.
"There is no need to think too much. We're benefiting from having him [Mbappe] because it's a great thing. Later, we have to find a solution to continue the adventure together."
Leonardo also confirmed PSG would keep faith with head coach Thomas Tuchel for next season.
Former Borussia Dortmund boss Tuchel has 12 months left on his contract and Leonardo said the club would have "time to think about" prolonging the German's stay in Paris.