Real Madrid are reportedly willing to pay a world record £161million to land the 18-year-old France striker, one of the hottest properties in world football.
But speaking at a press conference on Wednesday afternoon, Vasilyev said Monaco have accepted no bids and are hoping Mbappe will agree a new contract.
"I assure you that there is no agreement with a club," Vasilyev was quoted as saying on the club's Twitter feed.
"We are discussing a (contract) extension with Kylian. I hope that we will get there."
Mbappe rose to prominence last season when he scored 26 goals in all competitions as Monaco won Ligue 1.
A host of top sides have been linked with the teenage star, although Press Association Sport understands Manchester City are not one of them having not bid for Mbappe.
Bernardo Silva and Benjamin Mendy have already swapped the principality for the Etihad Stadium this summer in deals worth a combined £92million, but Mbappe will not be joining his former team-mates in Manchester.
Last week Monaco threatened to report ''important'' European clubs to FIFA for making contact with Mbappe without their consent.