The Portugal international's future at Old Trafford remains in doubt following the arrival of new manager David Moyes.
Nani has a year left to run on his current deal and the big-spending French outfit could offer him a lucrative move to the principality.
Claudio Ranieri has already splashed the cash by acquiring the likes of Radamel Falcao, James Rodriguez, Joao Moutinho, Eric Abidal and Jeremy Toulalan.
And Vasilyev has not ruled out a bid for the 26-year-old towards the end of the summer transfer window.
"He has been proposed to us," Vasilyev told French newspaper L'Equipe. "He is a very good player, but there have been no talks so far.
"We have already changed our group quite a bit and we also want to offer opportunities to our young players.
"We still have time to make a few alterations before the end of the transfer window, if needed."