The 16 year-old plays for Dijon's B team, which is in the French fifth division. Messi has scored three goals in nine league games this season.
L'Equipe says Rennes, Monaco and Marseille have their eyes on Messi, but it is Lille who are pushing the hardest to secure him.
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But also BlueCo, involving Chelsea and Strasbourg, are said to be keen on the 16-year-old.
Messi's contract with Dijon runs until the summer of 2025.