Arsenal have lost Alex Oxlade-Chamberlain to fellow Premier League club Liverpool and Man City are stepping up their pursuit of Alexis Sanchez with a reported £60m bid.
Liverpool and Barcelona have also expressed interest in the French international, with Liverpool bidding £74m earlier in the week as they prepare for the possible departure of Philippe Coutinho.
Earlier in August, Arsenal manager Arsene Wenger said that the possible deal with Monaco for Lemar was "dead".
The Gunners had made several bids for Lemar, the highest at £50m, but they were all rejected by the Ligue 1 champions.
Wenger said: "It's dead because Monaco has closed the door. They are still on cases like Kylian Mbappe and Fabinho.
"They've already lost Benjamin Mendy, Bernardo Silva and Tiemoue Bakayoko, so Monaco is at a stage where they have closed the door."
However, with the departure of Oxlade-Chamberlain and with Alexis Sanchez possibly following him out the exit door, Arsenal have now stepped up their pursuit of Lemar.