Arsenal were close to signing Lemar last summer, but they were unable to get a deal over the line, and Liverpool are set to try where the Gunners failed.
Arsene Wenger’s side are said to have moved on from Lemar, with other targets lined up.
Arsenal prefer Lyon’s Nabil Fakir now, and feel that he offers better value for money.
But Liverpool are convinced that they could bring Lemar to Anfield, if they can fund a deal.
Jurgen Klopp is keen to see the French international join his ranks, and the Mirror say that Monaco will be open to selling at the end of the season.
The Ligue 1 side lost a whole host of key players last summer, and decided that selling Lemar wasn’t in their interest.
But they could cash in on the wide-man at the end of the season, which is when Liverpool plan to swoop.