Aquilani has been a Liverpool player since 2009, but a disappointing injury-hit start to his debut season saw him sent out on loan to Juventus, but after the Turin-based side refused to sign the Italian permanently he was then farmed out to AC Milan.
However, the Roma youth-product did not convince the Rossoneri to make the deal permanent and his representative Franco Zavaglia believes a Liverpool stay could be on the cards.
"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 TMW.
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"The new manager [Brendan Rodgers] 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 has been plagued by injuries throughout his career, but Zavaglia believes the midfielder is currently doing well on the fitness front.
"Recently, apart from a slight ankle sprain, Aquilani has had no major fitness problems. The real problems were when he had ankle surgery at Liverpool."