The Rossoneri chief denied the club have reached an agreement to sign the goalkeeper and says he is pleased with the progress being made under Clarence Seedorf
The Cagliari goalkeeper - on loan at Chievo - is available on a free transfer in the summer and there had been speculation that the San Siro side had already secured his services.
However, Galliani has come out to say those stories are premature, but did hint the 29-year-old was a transfer target.
"Agazzi is an option, but it is not true that a deal has already been completed," the Milan supremo told reporters.
"He is a player out of contract in July, so we will see what happens then."
Milan clinched the signings of Adil Rami, Michael Essien, Keisuke Honda and Adel Taarabt during the January transfer window and Galliani says he hopes those arrivals can help inspire Clarence Seedorf's men to a European qualification spot in Serie A.
"Some teams above us lost at the weekend and if we'd have won we would have closed the gap a little," he added.
"It did not happen, but we hope it will in the coming weeks. The team is changing, we have changed formation, they are doing very well, the players are applying themselves and we are very satisfied."