The France international was at the centre of intense interest from both Arsenal and Liverpool during the recently-concluded transfer period, with the former even having a £92m bid accepted by Monaco.
However, Vasilyev has now revealed that Lemar was keen on joining either of the English top-flight teams, but that Monaco decided against allowing their star forward to depart this season.
“It was not easy,” Vasilyev said. “Thomas wanted to go to Arsenal and to Liverpool, but we had discussions and we took a communal decision so that he could stay here.
“He is a very important player for us. We could not have sold him, it would have affected the entire team and the individuals.”
Monaco already saw another star player depart the club following Kylian Mbappe's loan transfer to PSG, who have the option to make the deal permanent, for a reported £186m.