The Italian spent last season back in his homeland with a loan spell at Juventus, before returning to Anfield earlier in the summer.
There appeared to be a chance that he could stay with Liverpool after some impressive pre-season displays earned the praise of owner John Henry.
However, Fiorentina are still interested in signing the 27-year-old and some reports suggest a deal is close to being struck.
Aquilani's representative, Franco Zavaglia, claims the clubs have reached an agreement but insists the player has not yet made up his mind.
"The agreement between Fiorentina and Alberto has not yet been reached," Zavaglia told gazzetta.it.
"If we talk about an agreement, that was only reached between the two clubs, because Fiorentina (have not) come to any decision with us."