Osimhen, 21, enjoyed an excellent debut season in Ligue 1 with Lille and has been linked with a number top sides in Europe.
The Gunners, according to La Replubblica will however face stiff competition from Napoli who are in good financial shape to compete for his signature.
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Napoli are said to have identified Osimhen as a replacement for Polish forward Arek Milik.
Osimhen linked up with Lille from Sporting Charleroi last July.
The former Wolfsburg striker scored 18 goals and recorded six assists in 38 appearances across all competitions for the Great Danes last season.
Chelsea, Tottenham Hotspur Leicester City, Manchester United and clubs in Spain are said to have also expressed interest in signing the talented forward.
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