The Portugal international's contract expires next summer and the Ligue 1 club are reportedly considering cashing in on their prized asset during the winter transfer window, if they receive a sufficient offer.
The Gunners have made their interest known to Sanches's representatives, while Lille's hierarchy are also said to be aware, says Le 10 Sport.
But the Gunners boss could look to bolster his ranks in January as Granit Xhaka has been ruled out until the New Year with a knee injury, while Partey and Elneny will be missing as they head to the African Cup of Nations.
Arsenal are said to be 'very interested' in Sanches as they look to raid the January market for midfield reinforcements but are yet to make an offer.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!