However, the clubs still need to agree a fee, with Milan unwilling to meet Arsenal's £36m valuation of the Togo international.
Galliani says he has spoken to Arsenal boss Arsene Wenger about a deal but that they are "divided" on the player's value.
Milan said in June that Adebayor was their "sole transfer target" of the summer, although they later said they could not afford him.
After selling Alberto Gilardino to Fiorentina and with Ronaldo out of action because of a serious knee injury, Milan have made signing a striker their top priority, although Barcelona also covet Adebayor, who scored 30 goals in 48 games last season.
"If Adebayor decides to leave, Milan definitely want him but it is clear that if an offer arrives from Barcelona it would be difficult for him to say no," Galliani added.