The Gunners have reportedly had a first bid of £30m rejected for the 23 year old, but are looking at making another offer in order to land the French international.
Barca’s involvement in the race for Lemar may depend on their own battle to sign his France team mate Ousmane Dembele. The Borussia Dortmund winger is said to want to leave the German club this summer after the departure of manager Thomas Tuchel.
The Bundesliga side are however determined to keep hold of one of their prized assets, with a £79m asking price being placed on the former Rennes player.
Monaco are believed to be equally determined to keep hold of Lemar, after already selling Bernardo Silva to Manchester City, and also agreeing a £35m fee to sell midfielder Tiemoue Bakayoko to Chelsea.
Lemar scored 14 goals and provided an impressive 17 assists in 55 games for Monaco last season, and with Kylian Mbappe also on the radar of every top European club side, the Ligue One club may look to stop a fire sale by standing firm on the French winger.