The Gunners chased the Monaco winger throughout the transfer window but failed to land him.
Arsene Wenger made a number of bids for the 21-year-old early on in the summer before launching a staggering £92m offer on deadline day.
Lemar ended up staying put in France and his value is likely to go up even further if he continues to perform well.
Arsenal are confident they will be able to land the exciting attacker in the future but he could have already been a part of their squad.
Starsport understands Wenger and co shelved plans to land him for £60m earlier in the summer amid fears they were overpaying.
It is understood that the Gunners had worries about how much revenue he would bring them in comparison to his price-tag.
Despite that snub, Arsenal remain keen on Lemar and the player is interested in moving to the Emirates.
Starsport also understand the north Londoners will pull out all the stops to secure his signature this winter.
The Gunners have agreed a deal in principle with Monaco and settled on personal terms with Lemar.
The ex-Caen ace is set to sign a five-year contract worth around £250,000-a-week providing Wenger can get the deal done in January.
Lemar’s Monaco, who beat Marseille 6-1 before the international break, take on Nice tomorrow.
Arsenal, meanwhile, must bounce back from their successive Premier League defeats when they host Bournemouth this weekend.
