Lemar, 22, was the subject of a bid from Arsenal towards the end of the summer transfer period, agreeing a club-record £90 million deal on the final day, only for the midfielder to back out of it.
"He will stay at Monaco until the end of the season at 100 per cent," he told RMC.
Vasilyev said even if his club received huge offers for Lemar, there was no chance they would sell in January.
"If Liverpool or Arsenal come with a big offer before the end of the market? This is not relevant," he said.
"We will say no because the objectives are clear.
"Without important players like Lemar, we will not succeed."
Lemar has provided five assists and scored two goals in the league this season. He is contracted to the club until June 2020.