The 21-year-old has caught the eye this season and has bagged eight goals so far, including the winner in his club's 2-1 win over Tottenham in November.
Atletico Madrid and Bayern Munich have been also linked with the forward, while Italian champions Juventus are reportedly interested as well.
Now, according to L'Equipe, Manchester City have thrown their hat into the ring to sign Lemar in the summer..
Monaco are hoping to tie the France international down to a new contract but talks are currently at a stand-off.
Lemar cost Monaco around £3m, when they signed him from Caen in 2015, but they now want 10 times that amount if they allow him to leave.