The 22-year-old - who has been dubbed the ‘new Eden Hazard’ - has also been linked with Serie A giants Inter Milan and Juventus.
Lille sporting director Jean-Michel Vandamme said: "Boufal costs at least €20m (£15.6m), that's the minimum.
“In January it was impossible for him to be sold. We're not a club that sells in the winter window.
“In June there's a possibility that he may leave, though there are Premier League clubs after him too. I think the Italian clubs had better beat that competition by negotiating now."
Louis van Gaal eyes summer move for Aymeric Laporte
The Premier League suitors are thought to have asked to be kept informed about the England international’s situation as the Gunners prepare to offer him a new deal this year.
The 21-year-old Frenchman is thought to be among United’s key defensive targets, with Everton’s John Stones and Real Madrid’s Raphael Varane also on their shortlist.
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