Pre-season training begins on Wednesday for those players who were not involved internationally this summer, and with no interest from other sides the Italian, who has spent the last two seasons out on loan in Serie A, is expected back at Melwood.
AC Milan declined to take up their option to buy Aquilani after he failed to play the necessary number of matches to trigger his compulsory purchase.
New manager Brendan Rodgers will take time to assess all his available players but Aquilani's agent Franco Zavaglia would prefer to know quickly whether the midfielder, 28 on Saturday, has a future there.
"At the moment Aquilani is a Liverpool player and will certainly start pre-season training with them, then we'll see what happens," he told Tutto Mercato Web.
"The new manager will decide whether to keep him or not.
"I don't think he's coming back to Italy and he hasn't expressed any particular preference, but this time I hope Liverpool can tell us in time if he's not part of their plans so we can find him the right club."
Aquilani, who has two years remaining on his contract, has played just 28 matches for Liverpool as he arrived in August 2009 with injury problems which delayed his debut and then made it difficult to get into the team.
However, Zavaglia insists fitness issues are a thing of the past.
"Recently, apart from a slight ankle sprain, Aquilani has had no major fitness problems," he added.
"The real problems were when he had ankle surgery at Liverpool."
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.