Mbappe has been linked with a world-record transfer away from Monaco, having scored 26 goals across all competitions last season as his side unseated Paris Saint-Germain from their Ligue 1 throne and also embarked on a run to the Champions League semi-finals.
Real Madrid and PSG are among the clubs reportedly keen to prise the 18-year-old away from Monaco, but Jardim believes he will not follow stars Bernardo Silva and Tiemoue Bakayoko out of the club, although Benjamin Mendy is expected to join Manchester City.
"Mbappe seems very calm, he is young and has great potential," Jardim said during Monaco's pre-season tour.
"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."
The striker has already featured for Monaco in their pre-season campaign. He was given a 45 minute outing in their 4-2 win over Stoke City before playing for an hour as they drew 0-0 with PSV on Sunday.
While PSG and Madrid maintain their interest, Arsene Wenger appeared to concede defeat in Arsenal's pursuit of Mbappe on Saturday when he told reporters he expects the teenager to stay in Ligue 1 for another season.
"Maybe he had too much choice, so in the end people don't move," Wenger said.