Mbappe, 18, has been linked with a whole host of clubs, including Arsenal and Real Madrid, after scoring 26 times in all competitions for Ligue 1 champions Monaco during the 2017-18 campaign.
Last week, the forward admitted that he 'did not know' whether he was going to stay at Monaco in this summer's transfer window, but Jardim has said that he is "counting" on the teenager remaining with the club.
"Mbappe seems very calm, he is young and has great potential," Jardim told reporters. "He has only just joined up with the squad and so he needs to find his rhythm again, but I see he's doing well. I am counting on Mbappe as I am all of the players I have; I expect to have him here."
Mbappe was a part of the Monaco team that recorded a 4-2 win over Stoke City in Saturday's pre-season friendly, before also featuring in a goalless draw with PSV Eindhoven on Sunday.