Aquilani has been a part of Liverpool's pre-season tour of the Far East, but he is expected to be sold this summer as manager Kenny Dalglish attempts to balance his squad.
The arrivals of Jordan Henderson and Charlie Adam mean competition for places is fierce at Anfield ahead of the new campaign.
Aquilani spent last season on loan at Juventus after struggling in his debut Premier League campaign, but the Serie A club were not prepared to meet Liverpool's asking price.
Fiorentina have also shown an interest and the 27-year-old's agent, Franco Zavaglia, told Corriere Fiorentino: "Anything can happen, never say never. We will wait and see if there is anything concrete."
But Zavaglia acknowledges the reported £70,000-a-week wages which remain on the five-year contract Aquilani signed in 2009 could prove difficult.
He said: "Alberto has a major contract with Liverpool, and Fiorentina operate with certain economic parameters.
"I don't know whether the operation is feasible, but over time something (salary) can be skimmed (reduced)."