Teenage forward Mbappe has emerged as one of Europe’s most exciting prospects, while Portugal international midfielder Silva boasts an ever-lengthening list of suitors.
Vasilyev is, however, confident that services of both men can be retained, allowing Monaco to build towards a bright future.
He told Telefoot: "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."
Silva, who is said to be another target for those at Stamford Bridge, has made 48 appearances this term and contributed nine goals.