The teenage striker enjoyed a breakthrough season last year, scoring 26 goals to help Monaco conquer France and impress in the Champions League.
Mbappe is rated as one of the brightest talents in world football and has been the subject of interest from a number of clubs during the summer.
Zinedine Zidane is believed to be determined to bring the Frenchman to Real Madrid while Arsenal continue to be linked with a world-record move.
Monaco have already seen Bernardo Silva and Tiemoue Bakayoko seal summer moves to England but Jardim is confident that Mbappe will still be part of his squad next season.
‘Mbappe seems very calm, he is young and has great potential,’ Jardim, 42, 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 Gunners were strongly linked with Mbappe earlier in the summer but Wenger said over the weekend that he expects the 18-year-old to remain in France.
Kylian Mbappe’s Ligue 1 stats 2016/17
‘Maybe he had too much choice, so in the end people don’t move,’ the 67-year-old said.
With hopes of signing Mbappe fading, Arsenal have reportedly turned their attentions to his Monaco and France team-mate Thomas Lemar, who is valued at around £50million.