Liverpool and Arsenal both came close to signing the French international winger in August, but he decided to stay put at Monaco, despite the mass summer exodus in the club.
The two Premier League clubs will renew their interest during next month's transfer window but they now have a third competitor for Lemar's signature, with 'Telegraph Sport' reporting that Chelsea have entered the race.
According to the aforementioned source, Antonio Conte's side are preparing a bid of £80m next month to test the resolve of last year's Ligue 1 champions.
The 22-year-old was heavily linked with a move to the Premier League during the summer decided to stay at Monaco at the end of the window, even after the high-profile departures of a number of stars including Kylian Mbappe, Bernardo Silva, Tiemoue Bakayoko and Bernard Mendy.
However, after a disappointing start to the campaign for the Monagesque club, Lemar could be tempted by a move to the Premier League during the January transfer window, and he certainly won't be short of suitors.
The Blues reportedly have the advantage over Liverpool and Arsenal as they can offer players, either on loan or permamently, to move in the other direction. The club are also hoping the move of former technical director Michael Emenalo to Monaco can provide them with a boost in bringing Lemar to Stamford Bridge.