Mbappe is out of the France squad this week amid speculation that coach Didier Deschamps has unhappy with him partying in Sweden after pulling out of his previous squad due to injury.
But Konate said on Canal Football Club: "I often tell him: 'I want your level of football, but I don't want your life', because, frankly, it is difficult to bear having your name everywhere, for everything you do.
"When Mbappé is with us , we know the qualities he has, we know what he has brought to us and we should not be ungrateful for what he has been able to contribute to this French team and the whole world is aware of it.
"He is not here today. It is up to the players who are going to play in his position to do the job, be decisive and allow us to win games.
"It is the coach who makes his decisions. He is the one who decides whether he wants to call him up or not. I have no say in it."