The English winger has enjoyed a decent season on loan at Gefate in Spain this term.
But since United want to sell him due to off-field issues, Napoli are among the teams ready to bid.
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Italian newspaper Corriere dello Sport states that last season's Serie A winners will join the race for Greenwood.
Atletico Madrid, Gefate, Juventus, and two unnamed Premier League clubs have been linked to Greenwood in recent weeks by various outlets.
The forward has not commented on his future, with there still being a small possibility that he returns to United's first team.