The 26-year-old spent the whole of last season on loan at Juventus and impressed during his time in Turin.
A deal was in place to make the move permanent, but Juve refused to meet Liverpool's asking price and the Italy international has returned to Merseyside for pre-season training.
Aquilani's first-team prospects at Liverpool look doubtful with Reds boss Kenny Dalglish bringing in midfield duo Jordan Henderson and Charlie Adam this summer.
Aquilani's representative, Franco Zavaglia, admits the former Roma man wanted to stay in Italy, but he concedes a move now looks unlikely.
"Alberto's thoughts were to stay in Italy, but this was not possible," Zavaglia told Radio Sportiva.
"I don't know if there is a chance to go back to Italy during this transfer window, it's a shame our players leave Italian football.
"Liverpool are an important team and I think he can win the Premier League. The objective [at Anfield] is Champions League football."