The midfielder has been linked with both Premier League clubs in the summer after his fantastic 2016-17 for Monaco, and speculation continues to swirl about a potential exit.
A midseason move is not on the cards, though, with Vasilyev insisting any offers from the Reds or the Gunners would be batted away before Wednesday's transfer deadline.
"He will stay at Monaco until the end of the season 100 per cent," he told RMC (h/t Jacob Murtagh of Daily Mirror). "If Liverpool or Arsenal come with a big offer before the end of the market? This is not relevant. We will say no because the objectives are clear. Without important players like Lemar, we will not succeed."
According to Murtagh, both Liverpool and Arsenal have preserved an interest in the France international having failed to complete a deal for him in the summer window.
The 22-year-old is a huge talent and was a vital member of the Monaco side that impressed so many last season, as they surged to the Ligue 1 title and to the semi-finals of the UEFA Champions League.
Lemar's former coach Philippe Tranchant told football writer Tom Williams that Lemar has the class to play for any of European football's biggest clubs:
The youngster is on the right track, and while this season he's struggled to recapture the same highs as the previous term, his quality is still showcased frequently whenever he takes to the field for Monaco.
Lemar is accurate with his left foot, so he's able to provide tremendous deliveries from wide positions, thread delicate passes into small spaces and, when the situation demands, crack shots off at goal.
Factor in his pace and versatility, Lemar can bring a lot to a midfield. According to Sky Sports, Arsenal were willing to part with a staggering £90 million to bring Lemar to the Emirates Stadium in the summer.
According to Jonathan Northcroft of The Sunday Times, while Liverpool do have an interest in the young midfielder, they aren't dead set on pursuing a deal for him:
Jonathan Northcroft @JNorthcroft
Think what we should look at is the contrast with VVD, who Klopp was willing to pay world record for. VVD so much his No1/sole choice that he was a 'sign at all costs'. Lemar viewed differently: take him at right price but go another option (of which there are more) if not. https://t.co/XMjo7C6Tid
Staying at Monaco for the time being feels like the right decision for Lemar, as he still has raw facets of his game that he needs to improve.
The midfielder has been a little hit and miss when used centrally this season, whereas there are sometimes spells in matches when he hangs on the periphery of the game. Playing in familiar surroundings for the next few months will aid that natural development.
Monaco showed ahead of the current season they're willing to sell their best players for the right price, and it would be a surprise if interest in a star like Lemar was to fade away before the summer. If he goes to the FIFA World Cup and thrives, the Ligue 1 side will be able to put a massive price tag on him, too.