The Italian outfit have been negotiating a possible season-long loan for the midfielder, with the option of signing him on a permanent deal at the end of the league year. However, the 27-year-old is eager to secure a permanent deal now.
Franco Zavaglia, the player's agent, has insisted that talks for the former Roma star are ongoing, as he seeks a return to Italy after spending last season on loan at Juventus.
"The transfer is not at risk, and we remain with the possibility [of a move happening]," Zavaglia told La Gazzetta dello Sport. "There are no ultimatums as you never launch ultimatums in football.
"I don't know what has been reported in England, but I can say the player, having understood he is no longer a part of the plans at Liverpool, wants a permanent solution.
"But the deal is not at risk, we are just waiting."
Aquilani signed for Liverpool in 2009, but has made just 18 appearances for the club.