The midfielder, who is under contract with the Premier League side until June 2014, played on loan at AC Milan this season after failing to impress at Anfield.
"The new Liverpool coach will decide Alberto's fate," Aquilani's agent Franco Zavaglia said to Italian radio station Radio Mana Mana.
"We will have to wait and see what he thinks about the player and whether Alberto will be of any use to the Reds.
"Alberto has a contract at Liverpool for another two years and they will let us know about their intentions soon.
"He would be happy to stay at Liverpool if he was given the right opportunities."
The 27-year-old Aquilani moved to the Reds outfit in 2009 in a £20 million transfer deal from Roma.
He endured a disappointing spell at Anfield before being loaned to Juventus in the 2010/11 campaign.
Juve opted not to exercise the option to acquire Aquilani's sporting rights for a reported eight million euros last summer and the player joined AC Milan on a one-year loan deal instead.
Reports in Italy claimed Milan were keen to acquire Aquilani on a permanent transfer provided the player would terminate his contract with Liverpool.
However, his agent has denied those rumours.
"If Milan had wanted to sign him then they should have made their move sooner," Zavaglia said.
Aquilani scored one goal in 23 league appearances for the Rossoneri last season.