The Italian midfielder made 23 league appearances while on loan at AC milan last season.
The Rossoneri are looking to strengthen their midfield this summer.
“Before August 31, another midfielder will arrive, it could be Aquilani or somebody else,” Milan vice-president Adriano Galliani told Gazzetta dello Sport.
“We haven’t spoken yet to Aquilani. He is a Liverpool player.”
Aquilani’s current contract with Liverpool is set to expire in the summer of 2014.
