PA PhotosAquilani, 28, joined Liverpool from Roma for a fee of £20 million in the summer of 2009 but his first season at the club was ravaged by injury.
The midfielder then spent successive loan spells with Juventus and Milan in the 2010-11 and 2011-12 seasons, making 45 Serie A starts in total.
Though new manager Brendan Rodgers had stated he would be open to using Aquilani at Anfield this season, he has now sanctioned the sale of the Italy international.
Aquilani made only nine Premier League starts for Liverpool.
