The 21-year-old winger is high on Arsene Wenger’s wishlist this summer as he bids to bolster his squad.
Lemar is the man Wenger appears to be pushing for with doubts remaining over Alexis Sanchez and Alex Oxlade-Chamberlain’s future at the Emirates.
The Gunners saw their first bid of £30m rejected but, according to L’Equipe, they have returned with a second.
This time the offer could reach £35.2m when taking into account various add ons.
Arsenal are desperate to get the ball rolling on their summer activity and are also pursuing deals for Alexandre Lacazette and Kylian Mbappe.
But the Gunners have also seen a bid for both of those knocked back. The Mbappe one coming earlier in the window as they plan if another move is worth making.
Lacazette though was the subject of a bid this week which Lyon rejected.
Wenger is trying desperately to add quality to his squad after missing out on the Champions League for the first time since being in north London.
And Lemar impressed for Monaco last term as they won Ligue 1 and reached the Champions League semi-finals.
Tottenham also showed an interest early in the summer but have made little progress.
And Arsenal are ramping up their efforts with a second bid although Monaco are keen to keep the midfielder after already losing Bernardo Silva and with Chelsea closing in on a deal for Tiemoue Bakayoko.
