After scoring 26 goals in all competitions for Monaco last season, including six in the Champions League, Mbappe has been linked with Europe's biggest sides for months.
However, Vasilyev insists no transfer is close and says there is a chance he will opt to remain with the Ligue 1 champions.
"I assure you that there is no agreement with a club," he told reporters. "We have very important offers for Mbappe. He is the greatest talent in world football.
"We're discussing a contract renewal with him. I hope we'll get there."
While the France international is being linked with world record offers, there is a chance of an even more expensive transfer occurring during the current window, as PSG are hoping to trigger the €222 million release clause in Neymar's contract.