Lemar was long linked with a departure from the Ligue 1 club after playing a starring role in their title success and impressive journey to the UEFA Champions League semi-finals.
Moves to Liverpool and Arsenal were strongly mooted, as the two clubs looked to line up replacements for their respective wantaway stars Philippe Coutinho and Alexis Sanchez.
Those two ultimately remained in the Premier League, while Arsene Wenger claimed that Lemar rejected a move to London in favour of remaining in the principality, where he would have Champions League football to look forward to.
But Vasilyev – who revealed Arsenal were the closest to signing Lemar – was refreshingly honest when revealing the 21-year-old will likely be allowed to leave at the end of the season.
"Liverpool were really interested," Vasilyev told Sky Sports.
"But it was Arsenal that was really close to finalising the deal. It was quite close. At the same time it was just too late, not enough time to really follow up on this deal.
"Not all the elements of the puzzle fell in place. I'm very happy he stayed with us. For us, we need a player like Thomas Lemar. He's very important to our team.
"Definitely next summer [it] will be something to look at, although you know in football there are no guarantees.
"We had some players who were supposed to leave this summer but didn't leave because of X, Y, Z. I think it would be fair to say Thomas will have a fair chance to an exit next year.
"January? In football, never say never, but this is not what we're thinking of, this is really not in our plans.
"Then we have to wait and see how the team does in different competitions, if we have an interest in him and what his ambitions after the World Cup are. January doesn't seem like the right time for major changes in the team."
Vasilyev also accepted that Fabinho – another key player whom they managed to keep hold of for this season – may well be in his final season at Monaco.
"He's one of the key players in our squad, a very regular player," he said. "He's very important, we can always count on him.
"We are very happy that we managed to keep him. I think this is one player you want to keep forever.
"But we realise in Monaco that we have a certain model, that at a certain moment when we feel it's right we have to let players go in order to be successful again.
"This is not only about money; this is more about being successful."