Ever since the closing weeks of the summer transfer window, Lemar has been strongly linked with a transfer to the Premier League but Monaco have maintained that the French international is not for sale.
However, with Lemar continuing to show no desire to pen a new contract at Stade Louis II, it appears that the Ligue 1 outfit will receive more approaches at the end of the campaign.
According to The Independent, Liverpool boss Jurgen Klopp remains interested in the player and is prepared to give the green light for another sizeable bid.
The Merseyside giants opted against bringing in a direct replacement for Philippe Coutinho in January but Lemar - valued in excess of £80m - is said to be at the top of their shortlist ahead of next season.
Lemar has contributed just two goals and five assists in 19 Ligue 1 and Champions League matches during the current campaign.