Mbappe has less than a year remaining on his contract at the Parc des Princes and is yet to agree a new deal.
The 22-year-old was courted by Real Madrid in the summer transfer window but PSG rejected a series of bids from Los Blancos.
On the pitch, Mbappe continues to impress for Mauricio Pochettino’s men, with four goals and two assists in five Ligue 1 games this season.
"I don't see Mbappe leaving at the end of this season. Nobody is thinking about the future of Paris Saint-Germain without Kylian," the PSG director told Canal Plus.
"Kylian sort of represents the difference between the superficial and the deep. Kylian's relationship with Paris Saint-Germain is deep. That's why we don't think about anything else.
"Kylian represents many things. Not only because he is French or one of the best players in the world. He has a way of being that we like and one that everyone likes."
"We were not happy with the behaviour of Real Madrid," Leonardo added. "Starting negotiations for one of the best players in the world in the last week of the transfer market generated a situation that we did not like.
"We were clear about our position with the offer. It was not enough, it was smaller than what we paid. The last offer they talked about never came. You can't organise a transfer market for two, three or four months and change your plans like that."
