The 18-year-old Frenchman is attracting attention from all quarters of the football world, with numerous elite clubs believed to be keen on sealing his signature.
Mbappe has also proved his talent on the Champions League stage having netted five times in the tournament, helping the club to reach the semi-finals.
Vasilyev has played down talk of one of Monaco's prized assets moving elsewhere, adding that in-demand Bernardo Silva is also likely to stay put.
"No player has told us they want to leave," Vasilyev told Telefoot. "Of course, we will talk with the players, but with the World Cup taking place in 2018, Thomas [Lemar], Kylian nor Bernardo would not want to leave.
"But this is not the time for discussions. We will do everything to keep them. One thing is for sure - Monaco will have a very competitive team next year."
Mbappe made his senior debut in 2015 after joining the club's academy two years prior.