Aquilani arrived at Anfield from Roma in 2009 but his first year at the club was blighted by injuries and he has spent the past two seasons in Italy
The Italy international spent last season at San Siro but is now scheduled to return to Anfield for talks with new boss Brendan Rodgers over his future with the Merseysiders.
According to Corriere dello Sport, Milan want to extend Aquilani's loan deal for another 12 months, but Liverpool are only willing to entertain the idea of a permanent transfer for a player who has two years left on his current contract with the club.
The paper claims, however, that there is a possibility of the Reds terminating Aquilani's contract as it would save them approximately €12 million in wages.
The third option is Aquilani remaining at Anfield, but the newspaper insists that this is the most unlikely outcome.
With Fiorentina not in a position to meet the midfielder's wage demands, and new Roma boss Zdenek Zeman said to have no interest in bringing the 27-year-old back to the Stadio Olimpico, there appear to be no other alternatives for Aquilani.