The Denmark international has been made available by United, with AC Milan also in contact.
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However, the Serie A champions are now in talks after losing Romelu Lukaku to a serious injury last week.
Transfer expert Fabrizio Romano is reporting: "Napoli have made new contact with Man United today for Rasmus Hojlund deal.
"Hojlund’s camp also in talks with Napoli as player’s keen on the move while also wants guarantees to stay at the club in future, not a simple loan. Negotiations ongoing."