Just 18, the winger has enjoyed an outstanding first full season of senior football in Ligue 1.
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In 15 appearances, Cherif has scored three goals and is attracting interest from across Europe.
Tuttosport says Milan are lining up a January move for Cherif, who also has the likes of Stuttgart, Borussia Monchengladbach and Eintracht Frankfurt also keen.
Cherif has a deal to 2028 and is a former France U18 international. Milan have stepped up their scouting of the teen in recent weeks.