Alberto Aquilani's agent says the midfielder is still waiting to find out if he has a future at Liverpool.
Aquilani, who turns 28 this weekend, signed for the Reds in 2009 while Rafael Benitez was in charge, but his successors, Roy Hodgson and Kenny Dalglish, both allowed the Italian to go on season-long loans to Serie A clubs.
Brendan Rodgers has indicated in a radio interview that he is keen to work with Aquilani, but agent Franco Zavaglia said there has not been any decision as yet.
"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."
Zavaglia also said Aquilani, who has two years left on his contract, has overcome the injury problems that plagued his debut season at Anfield.
"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."
Meanwhile, Liverpool midfielder Lucas Leiva has revealed he feared for his future after suffering anterior cruciate ligament damage last year but hopes to return for the start of the new campaign.
"The most difficult period for me was when I was on crutches for two months, especially the first four weeks after the surgery when the knee was swollen," he told Press Association Sport.
"To be honest in a few moments I thought I couldn't come back any more or even walk because the way I looked at my knee I felt scared, but as soon as I started the rehab it is unbelievable how your body reacts.
"My main target now is to be 100% recovered and be okay to play a part in next season."
He added: "I think I am progressing very well in terms of the knee, strength and fitness-wise. I am working every week and trying to improve every week and the main target is to be fit for the new season - if not for the start then after a few weeks.
"And I think maybe this six to eight months I will add on at the end of my career. I am confident I will be back at the same level because I know how hard I am working."