The England international spent last season on-loan at Arsenal, but struggled to make an impact.
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Transfer expert Fabrizio Romano is reporting Sterling has now been offered to Napoli.
The Azzurri are in the market for a new winger signing and given the success of ex-Premier League players Scott McTominay, Billy Gilmour and Romelu Lukaku, Napoli management are now seriously considering adding Sterling to Antonio Conte's squad.
Kevin de Bruyne, who played with Sterling at City, has already arrived this summer.
Along with Napoli, Bayer Leverkusen are also considering Sterling, who has been made available by Chelsea this summer.