They are looking for a long-term replacement for Andres Iniesta, and with their pursuit of Philippe Coutinho continuing to be frustrated by Liverpool, are now considering Lemar instead.
Monaco midfielder and Arsenal target Thomas Lemar is on Barcelona's radar, say reports
Arsenal almost signed Lemar on transfer deadline day in the summer for a club record £90million, and although the deal fell through the Gunners remain keen.
There is a complication, however, in that Arsenal were only able to bid £90m after accepting a bid for Alexis Sanchez, which also fell through.
Sanchez is set to leave on a free next summer, along with Mesut Ozil, with both showing little inclination to extend contracts that expire in 2018. The situation leaves the Gunners short of funds.
Arsene Wenger will go back in for Lemar next summer and the club are confident they are in pole position to do a deal with Monaco, according to The Mirror.
With Barca's pursuit of Philippe Coutinho frustrated by Liverpool, they are considering Lemar
They will face a battle though, with the player's advisers knowing he is one of the hottest properties in European football and he can command a huge contract in excess of £250,000-a-week.
It is understood Liverpool are another team interested in bringing the highly-rated France international to the Premier League.
Lemar has made 13 appearances in all competitions for Monaco this season, managing just one goal in the league.