The Gunners were ready to shatter their transfer record on deadline day last summer, making a £90m (€100m) bid for Lemar but failed to get the deal over the line in time. Liverpool also emerged as a serious contender to sign the 22-year-old late on, making two bids in the final week of the window, but it was Arsenal who came closest to striking a deal, as later revealed by Monaco vice president Vadim Vasilyev.
Since the summer transfer window closed, Vasilyev has admitted he expects Lemar to leave next summer –but Arsenal may move onto other targets by then.
According to The Mirror, Arsene Wenger's side are now fearful a deal will be "impossible" given growing interest from Champions League clubs who will be ready to offer the player a better deal.
Liverpool may find themselves flush with cash should Philippe Coutinho complete a move to Barcelona, with Lemar a possible replacement for the Brazil international.
The report adds that Arsenal are already looking at alternative options, with Lyon playmaker Nabil Fekir chief among those. The France international has produced a stunning return of 12 goals and three assists in 15 appearances this season and could be the next high-profile departure from Lyon, following Alexandre Lacazette's club record exit last summer.
Arsenal are facing the increasingly likely prospect of having to rebuild their attack next summer with Alexis Sanchez and Mesut Ozil both expected to leave the club in the near future. Both players can leave on free transfers when their contracts expire at the end of the season, unless the Gunners decide to try and cash in on the pair while they still can in January. Alexis Sanchez is said to have already decided on his next club, thought to be Manchester City, while Mesut Ozil remains heavily linked with a reunion with Jose Mourinho at Manchester United.