Manager Antonio Conte is weighing up a lucrative bid for the 22-year-old, which would see their previous transfer record (£57m for Alvaro Morata in the summer) broken.
Chelsea could offer £80m to bring Lemar to Stamford Bridge next month, although Arsenal and Liverpool remain interested parties and could make counter offers.
The Blues feel their former technical director Michael Emenalo being at Monaco could help them in their pursuit of the French international, but the French club were previous opposed to letting any more key players leave.
However, with Monaco eliminated from the Champions League, and nine points adrift of Paris Saint-Germain in Ligue 1, Lemar might feel he needs a new challenge with a side challenging for major honours.
It would be more bad news for Arsenal, who came close to procuring his signature in the summer. The Gunners looked set to sign Lemar when Alexis Sanchez almost joined Manchester City, but now they risk losing out on him entirely.
His reported £80m asking price might prove too steep for both Arsenal and Liverpool, but Chelsea are desperate for strength in depth given their lack of numbers this season.
Lemar has scored and created four goals in 10 Ligue 1 starts this season, creating 23 chances. He could have offers coming his way in January.
Stats from Transfermarkt.