The Reds have a deadline of June 30 to hand over 5million euros (£4.4milllion) to the Serie A oufit.
That will take the total outlay for Aquilani, who was signed by Rafa Benitez in August 2009, to 20million euros (£17.6million).
Aquilani hasn’t pulled on a Liverpool shirt since the Europa League qualifier against FK Rabotnicki last August and the Italy international is unlikely to play for the club again.
The 26-year-old spent the season on loan at Juventus after an injury-plagued first year at Anfield.
The Reds hoped Juventus would sign Aquilani on a permanent basis but they have so far been unable to agree a deal.
Juve failed to take up their option to buy him for £14million and the Echo understands they were only willing to offer around £6million.
