The Italian midfielder failed to make an impression when he arrived at Anfield three years ago and has since been on loan back in his homeland, first at Juventus then AC Milan.
New manager Brendan Rodgers has said: "I thought he was a really, really good player. Obviously he came to Liverpool and it didn't work out and he's gone back on loan. He's a wonderful talent, a terrific player.
"He might just not be able to settle, he might not be able to adapt to the country, so you've got all those issues and obviously sometimes you're not aware of that until you speak to them."
It is believed that Liverpool are prepared to sell Aquilani for as little as £3m (a lot less than the £20m they paid AS Roma for him) to get him off their books.
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