The Mail on Sunday says the Italians made their first move for Manchester City's powerful African forward earlier this week when the two clubs met to consider an offer for AC's Brazilian forward Alexandre Pato.
The bid for the 20-year-old was dismissed by Milan vice-president Adriano Galliani, who then enquired about Adebayor, the highest-paid player on the Eastlands staff.
Milan accept the Togo international will cost them at least the £25million City paid Arsenal for him a year ago.
Judging by the approach the Eastlands club made for Nikola Zigic before the Valencia striker joined Birmingham for £6m, however, it is clear they are prepared to offload Adebayor. He scored 14 goals in 25 Premier League appearances last season.