Talks over a potential switch were thought to have collapsed after the Italy international said he would prefer a permanent move rather than a loan deal and Fiorentina were unwilling to meet the Reds' asking price.
Aquilani's agent, Franco Zavaglia, says the 27-year-old, who spent last season back in his homeland on loan at Juventus, does not want to be loaned out only to face the same situation of negotiating his future again next summer.
And Zavaglia claims the Viola are still weighing up whether to sign the former Roma man on a permanent contract.
"As Alberto doesn't yet fall in the plans of Liverpool, we want to find a solution so that next year the current situation will not reoccur again," he told Sportitalia.
"The player wants to come to Italy on a definite transfer.
"I met (Fiorentina's sporting director, Pantaleo) Corvino, and the club must think about it. It's a difficult deal, but let's see.
"There is a 50 per cent chance that my client will transfer to Florence. Last year in August there was 'magic', let's see if this year will be the same, there is still time."