Mbappe is into the final year of his contract at PSG and he is still yet to pen fresh terms at the Parc des Princes.
Real Madrid are keen to sign the France forward and they failed with approaches for him during the summer transfer window.
The Spanish side are expected to return in January, when they can talk to the 22-year-old about joining them for free in July, but Leonardo still thinks Mbappe will stay put and sign a new deal.
“The fact that he’s staying, that was the only thing that could happen. We never thought about doing all this without Kylian. We were not happy with the behaviour of Real Madrid,” Leonardo told Canal Plus.
“We were clear about the offer they made. It was not enough from our point of view. It was less than what we paid. As for their last offer, it never arrived.
“I don’t see Kylian leaving at the end of this season. Mbappe’s relationship with PSG is deep. I don’t think anyone here sees the future without him.”