Daily Mirror are reporting that Arsene Wenger is a huge admirer of the 21-year-old and wants him to join the Gunners for next season.
Lemar has had a sensational season with Monaco so far and has bagged 14 goals and 11 assists for the Ligue 1 side.
The highly talented 21-year-old can operate in a number of positions. Although he has played on the left this season, he can play on the right and in behind the striker as well.
Lemar has impressed in the Champions League this season and has already won two international caps. He joined Monaco in 2015 and it will be tough for the Gunners to persuade the French outfit to sell this summer.
The Frenchman is valued in excess of £25million right now and although the fee might not be a problem for Arsenal, they will find it tough to convince the player without Champions League football. The Gunners are currently fifth in the table with just three matches remaining.
Meanwhile, Daily Mirror are reporting that Arsenal are confident of signing Sead Kolasinac this summer.
The 23-year-old Schalke left-back is out of contract and will join the Gunners on a free transfer.
Wenger is interested in the likes of Virgil van Dijk and Alexandre Lacazette as well.