Mbappe, 18, scored 15 times on Monaco's remarkable run to the French title last season but has been constantly linked with a move away from the principality over the summer.
Real Madrid and PSG are both reportedly desperate to sign the young France international, who is valued at 180 million euros ($212 million).
It is understood that the player himself favours joining PSG, where he would team up in attack with Neymar, signed last week for a world record 222 million euros. Mbappe hails from the Paris suburbs.
On the possibility of Mbappe joining the club Monaco pipped to the Ligue 1 crown in May, Jardim recalled the day "a leading director of a Portuguese club, with whom I had a meeting, said to me: 'The transfer market is not just made to strengthen your team, but also to weaken your rivals.
"I think that is a strategy used by many. But I am staying calm."
This summer Monaco have already sold Tiemoue Bakayoko, Bernardo Silva, Benjamin Mendy and Valere Germain, all key players in their run to the title.
While they appear weakened as a result, they have made a host of new signings, including this week recruiting Algerian international winger Rachid Ghezzal, who was a free agent after leaving Lyon. The transfer window shuts at the end of this month.
"I am waiting calmly for the 31st. I like to make the most of each day...we are here to make the best of Monaco," added Jardim, whose team visit Dijon in Ligue 1 on Sunday.
Jardim also evaded a question as to whether Mbappe had informed him of a desire to leave the Stade Louis II.
"The players come to talk to me. I have private conversations with all of them. I try to listen to all of them about their objectives and ambitions.
"It is something I try to do about once a month. And it is not just the case for Kylian."
Mbappe has started both of Monaco's games so far this season, although he didn't score in the 2-1 Champions Trophy defeat to PSG or in last Friday's 3-2 win over Toulouse that began their title defence.
So is he disturbed by all the talk about his future?
"The start of the season differs for every player. Every player has a different way of reaching the top of his form. After that, when there is a lot of movement in the transfer market, the players cope with more or less difficulty. But that is how it is."