The 19-year-old has emerged as one of Europe’s most talented young players in recent months and has subsequently seen his stock rise.
United, and a number of other European clubs, have been linked to the forward as Monaco continue to impress on both the domestic and European stage.
But vice-president Vadium Vasilyev has said that Mbappe, alongside the highly-sought Bernardo Silva, have offered no indication that they want to leave Monaco.
Speaking to Telefoot, he said: "No player has told us they want to leave.
"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, who has also attracted interest from Chelsea, Arsenal and Manchester City, has netted 22 times in all competitions this season.
Silva, who is said to be another Stamford Bridge target, has made 48 appearances for Monaco this term and contributed nine goals.