The 38-year-old striker confirmed his departure from Los Angeles Galaxy last week following the club's elimination from the Major League Soccer playoffs.
Gazzetta dello Sport and Sky Sports Italia reported that the former seven-time European champions have now made contact with the player's agent Mino Raiola.
The US-owned club want the former Swedish international for six months and are prepared to pay him six million euros ($6.6 million) if he remains for 18 months in total, Gazzetta claimed.
Milan finished fifth last season, missing out on a return to Champions League football by just a point to city rivals Inter.
They have had a poor start to this campaign and are 14th after 12 games before they host last year's runners-up Napoli on Saturday in the San Siro. Ibrahimovic played for two seasons between 2010 and 2012 with AC Milan, helping them to their last Serie A title, and scoring 42 goals in 61 league appearances.
He also won three league titles with Inter Milan, and two with Juventus, which were both revoked following the 'Calciopoli' match-fixing scandal.