The Premier League duo, whose links with Lemar in the summer transfer window have continued in January, have both cooled their interest in the French international.
Vasilyev told French radio station RMC that any late bids before the close of the current window will not be considered.
"[Lemar] will stay at Monaco until the end of the season, 100%," the vice president said. "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."
Liverpool were reportedly keen to sign a replacement for Barcelona midfielder Philippe Coutinho, although Reds boss Jurgen Klopp has suggested that the club are not interested in immediate replacements.