Like the bulk of Monaco's big guns, he attracted serious interest over the summer but despite being heavily courted by Arsenal and Liverpool, stayed put with the Principality side, who have struggled this term and were knocked out of the Champions League in the group stage.
Arsenal and Liverpool maintain an interest in the 22-year old, but Chelsea have entered the race, as per L'Equipe.
But Telegraph Sport can reveal that Chelsea hold a strong and genuine interest in Lemar, and are seriously considering making a bid of their own.
The Blues would have to break their transfer record of £60m, which was spent on striker Alvaro Morata.
However, Chelsea are also said to be interested in signing the French worldwide as Antonio Conte looks to improve his squad when the transfer window opens.
Lemar was keen on a move to the Premier League last summer but Monaco rejected a £72m bid from Liverpool and a move to Arsenal failed to materialise as it was dependent on Alexis Sanchez joining Manchester City on deadline day.
Lemar's contract runs out in 2020 and it is likely that he will wait until the summer to move despite Monaco having dropped out of the Champions League and looking highly unlikely to defend their Ligue 1 title against a powerful Paris Saint-Germain side.
Lemar himself is said to be ready to consider an exit from Monaco, irritated by the club's hard season, especially in the Champions League.