The 27-year-old is surplus to requirements at Anfield and initially appeared to be on his way to Fiorentina.
Fiorentina would prefer to take Aquilani on loan, while the player has set his sights on a permanent move. Although the Italian's agent is adamant that the deal could still go ahead, the midfielder is believed to be looking at other options and would be open to a move to San Siro.