Pre-season training began for those players who were not involved internationally this northern 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 its option to buy Aquilani after he failed to play the necessary number of matches to trigger his compulsory purchase.
"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
Aquilani, who has two years remaining on his contract, has played just 28 matches for Liverpool as he arrived in
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."
David Moyes had no hesitation in rubber-stamping Rio Ferdinand's one-year contract extension because he believes the Manchester United defender has just had one of his best seasons ever.