Reports emerged claiming that the transfer fell through because Lemar did not want to play for Arsenal due to the club being absent from the Champions League.
Liverpool, who will be playing in the elite European competition this season, were also heavily linked with a late approach for the Frenchman, but Vasilyev has suggested that Lemar stayed due to the club already allowing a handful of first-team players to leave.
"It was not easy," The Independent quotes Vasilyev as saying. "Thomas wanted to go to Arsenal and to Liverpool, but we had discussions and we took a joint 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."
Wenger has confirmed that he will revive his pursuit of Lemar when the transfer window reopens.