The 22-year-old is wanted by both Premier League clubs, who have been tracking him for the past year.
Monaco are desperate to keep their star forward, and they want him to sign a contract extension.
But, according to L'Equipe, Lemar has rejected the chance to agree terms with the French champions.
The France international reportedly wants to keep his options open and therefore he
won't sign a new deal.
A report published by L’Equipe showed how Lemar is not even in the top 30 highest paid players in Ligue 1.
Lemar's current contract is due to expire in the summer of 2020.