The Croatia international has been frozen out of the Juve squad by coach Maurizio Sarri this season.
He was left out of the club’s Champions League squad and is yet to feature for the Old Lady in Serie A in 2019/20, as they look to find him a new club.
Manchester United have been strongly linked with a swoop for the 33-year-old to bolster their misfiring attack in January.
However, Italian outlet Il Giornale reports that they have been beaten to the punch by Milan, who have already agreed terms with the striker.
The outlet claims that Milan’s city rivals Inter were also interested in Mandzukic, but Juventus preferred to do business with the Rossoneri.
An agreement has been reached between the player and the club over personal terms, ahead of a possible transfer in January or next summer.
Like United, Milan are desperate to inject some attacking flair into their side after struggling for goals this season.
Ole Gunnar Solskjaer’s side have scored nine goals in eight Premier League games, leaving them just two points above the relegation zone as things stand.
Milan haven’t fared much better, finding the net six times in seven Serie A outings to leave them hovering three points above the drop zone.
The Italian giants took action before the international break by sacking coach Marco Giampaolo and replacing him with Stefano Pioli.
Mandzukic helped Croatia reach the World Cup final in 2018 before going on to score 10 goals in 33 games across all competitions for Juve last season.
Deployed through the middle and on the left wing by former Juventus coach Massimiliano Allegri, he helped the club win four Scudetti in four years since his arrival from Atletico Madrid in 2015.
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