Aquilani has struggled with injuries but has recovered from ankle surgery and is yet to start a game for the Reds.
But Liverpool boss Rafa Banitez says he is likely to name the Italy international on the bench for the home match with Manchester City on Saturday.
He said: “Alberto wants to play for us and he is so desperate to be involved as quickly as he can but he understands the reasons he cannot start yet.
“He wants to keep improving his condition and now it is just a matter of him keeping calm as it will not be long before he is there. He is pushing us all the time.
“He is very positive and wants to help the team now but you must remember that we have a responsibility to him, and we will not take any risks at this stage.
“We have got to keep analysing the situation and watching him in every training session but we know that the right time is nearly here. He has a very good mentality.”
He added: “You can see in everything he does that he has got quality.
“He knows when to pass at the right time and to the right players, he makes good decisions on the pitch.
“Alberto is training really well and he is doing extra work to make sure he is in the best possible condition; I spoke with him in the gym this week and he is very positive, his spirits are good.
“We have meetings every day with our medical staff to see how much we can keep pushing him and when the time is right to increase the levels of his work.
“He is a player who can pass the ball and we have seen that in the games he has played so far, even though he has not had too much time on the pitch.”