Reports suggest the Blues are lining up a £70million offer for Silva, 22, with Antonio Conte scouring the market for midfield reinforcements ahead of the summer transfer window.
The Portugal star, also wanted by Manchester United, has scored eight goals and notched up five assists for Monaco this season and the Ligue 1 giants are desperate to keep hold of him.
However, when asked if there have been inquiries for Silva, Vasilyev told The Times: ‘Yes, yes. I really don’t want to go into details, but for all our major players, we do have interest from major European clubs.
‘This is not the right time to talk about it. Let’s finish the season and then we can look at our project for next season.
‘Me, the coach and the players are focused on this season.’
It’s understood Chelsea boss Conte is also keen on Silva’s Monaco team-mate Tiemoue Bakayoko.