TalkSPORT says agents for the former Chelsea attacker have made contact with United about his availability.
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It's been suggested a loan-to-buy arrangement has been proposed by intermediaries.
Loftus-Cheek is also interesting Aston Villa, where it's just been confirmed Boubacar Kamara is out for the season due to injury.
Under contract to 2027 at Milan, Loftus-Cheek has made 23 appearances this season, scoring once and making one assist.