They could allegedly face competition from La Liga club Atletico Madrid, who may need to find a replacement as star striker Antoine Griezmann continues to be linked with a move to either Barcelona or Real Madrid.
However, the English newspaper claim that the 22-year-old would prefer a move to England rather than Spain as he looks for a transfer away from Ligue 1.
Jurgen Klopp and Arsene Wenger are reportedly admirers of the Frenchman, who is known for his versatility at being able to play on both wings and through the centre which is an essential quality given the top Premier League clubs can play a game every three days.
Lemar joined Monaco in 2015 from Caen and has since made 108 appearances for the French club, scoring 22 goals.