Milan are hoping to land the Italy international as they look to bolster their midfield line before the start of the season.
"I will remain here, in Liverpool, until I complete the transfer in favour of AC Milan," said Aquilani's agent Franco Zavaglia to Gazzetta.it.
"Aquilani has chosen and he wants AC Milan. We hope an agreement will be reached very soon."
Aquilani, who spent last season on loan at Juventus before returning to Anfield earlier this summer, is under contract with Liverpool until June 2014.
AC Milan begin their Serie A title defence at Cagliari on Saturday.