Obinna is coming to the end of a season-long loan from Inter Milan but is out of contract at the Italian giants in the summer.
The 23-year-old Nigerian spent last season on loan at Spanish outfit Malaga and has scored eight goals for the Hammers this term.
Italian job: Obinna fancies plying his trade with Napoli next season
But he is ready to return to Serie A and Valentino Nerbini, the player's agent, said: 'Obinna hopes to come to Napoli, which is a place he has always liked.
'A few years ago, a deal was in place to take him there for around ?5million. However, the deal broke down over problems relating to image rights.
'Now that Obinna could arrive on a free transfer, Napoli would be crazy not to take him. The dream is to come to Napoli, a club who are playing beautiful football at the moment.'
The team from southern Italy are six points behind AC Milan with five games to go in the race for the title.
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