The 23-year-old wants to leave the Reds, according to reports in the media, and have still not signed a new deal with the club.
“We are going to sign a new defender in January, there’s is no doubt about that,” Milan vice-president Galliani told Denmark’s tipsbladet.dk.
“We have kept a frequent eye on Agger and his situation at Liverpool and have of course noticed the problems that Agger and Liverpool have on agreeing on a new contract.
“We have a list of three or four names that could be used in the defence. Agger is one of those names.
“We will for sure make a bid for one of them in January.”