Lemar, 21, has been the subject of two offers from Merseyside over the last 48 hours, according to L'Equipe. While Monaco are adamant the France international is not for sale this summer, the Merseyside club appear determined to test their resolve and have offered €80m plus Divock Origi on a one-year loan deal to try and tempt them into doing business before Thursday's transfer deadline.
Monaco's Ligue 1 triumph last season, coupled with their impressive run in reaching the Champions League semi-final stage, saw their bright young squad become the envy of Europe.
Benjamin Mendy and Bernardo Silva, two key players under Leonardo Jardim last term, have both left the Stade Louis II to join Manchester City with Kylian Mbappe, the jewel in the Monaco crown, now expected to join domestic rivals Paris Saint-Germain.
Bakayoko was also part of the exodus, joining Chelsea for a reported £36m. But while Mbappe looks set to be the next high profile player to leave the French champions, the Blues midfielder does not believe Lemar will follow suit.
"Having talked a bit with him last season, he is more or less staying," Bakayoko told SFR Sport.
Liverpool will be hoping to change that in the coming days. L'Equipe understand the Reds have returned with a new offer; €50m up front with a further instalment of €30m to be paid next summer for Lemar in addition to offering Origi's services. The Premier League side are now awaiting a response from Monaco vice-president Vadim Vasilyev.
Arsene Wenger, who had been determined to sign the player "at all costs" earlier this summer, has even admitted defeat in prising him away from the principality.
"It's dead because Monaco has closed the door definitely," Wenger told reporters last week.