The French publication reports that the winger has turned down several opportunities to sign a new deal with the Ligue One club since joining in 2015.
The 22 year old may consider offers from a number of European clubs after the tournament, giving Arsenal the chance to finally secure the signing of the Frenchman.
The Gunners tried to sign Lemar back in August, but were scuppered in their attempts as time run out on transfer deadline day to complete the deal. They chose not to renew their interest in January with Monaco unwilling to let players leave mid season.
It was also reported by the Mirror that the player had a £90m price tag, but this could be reduced in the summer if the player is adamant on leaving and refuses to sign a contract extension.
Arsenal are not the only team interested in Lemar, with Liverpool and Chelsea also having been heavily linked with the winger in recent months.