The Rossoneri are looking to sign another centre forward after Giampaolo Pazzini suffered a serious injury and they have attempted to lure Carlos Tevez to San Siro.
However, with the Argentine looking closer to Juventus at the moment, Milan officials have turned their attention to Udinese veteran Antonio Di Natale.
The Rossoneri have already held a meeting with the player and his agent, where they have been informed the striker would be interested in joining the club.
Di Natale, who has one year left on his deal with the Zebrette, is disappointed not to have been offered a contract extension at Fruli and could in turn request a summer transfer.
Despite turning 35 last October, the former Italy international has enjoyed another impressive season, having scored 23 goals in 33 league matches for Udinese.