The Italy midfielder is contracted to the Anfield club until June 2014, but he has spent the last two seasons on loan back in his homeland with Juventus and most recently at AC Milan.
"We had a meeting with English executives but for the time being, nothing has emerged," Aquilani's agent Franco Zavaglia told Il Sussidiario.
"We expect a response from Liverpool which should arrive within the week."
Aquilani reportedly has the option to terminate his Liverpool contract and move wherever he pleases as a free agent, something Zavaglia insists is not an option for the 27-year-old.
"There is absolutely no possibility that Aquilani can become a free agent in order to then decide what to do," Zavaglia added. "I don't know if he wants to stay at Milan, we shall see. We just have to wait and see what happens and what Liverpool decides."
The prospect of a return to Milan on a permanent basis has been made more difficult for Aquilani as the Rossoneri have already signed Riccardo Montolivo on a free transfer.
Aquilani joined Liverpool from Roma for a £20 million fee in 2009, but an injury-plagued year at Anfield saw him start just nine Premier League games in England before he embarked on his two loan spells back in Serie A,