Lemar's Monaco future had been in doubt all summer, with Arsenal initially appearing as frontrunners to land the Frenchman's signature.
However, the Gunners failed to conclude a deal midway through the summer, allowing Liverpool to try their hand at prizing the winger away from the French champions.
A frantic end to the transfer window saw Monaco reject two bids from Jurgen Klopp's side, but finally accept a £92m club-record offer from Arsenal on deadline day.
In the end, Vasilyev confirmed that a communal decision was taken to keep Lemar at the Stade Louis II. He told 'TASS':
"It was not easy. 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."
Since the deadline day madness, Arsene Wenger has confirmed Arsenal have not given up on signing the 21-year-old, but is aware that he may face tough competition from Liverpool.