The 20-year-old is keen for a move away from Anfield, with Manchester City expected to make a fresh bid for his services after having two offers turned down.
He fuelled speculation about his future by skipping training sessions on Wednesday and Thursday after he had a meeting with boss Brendan Rodgers at Melwood earlier in the week.
Sterling reportedly told the manager he was unwilling to go on the club’s preseason tour of the Far East and Australia.
Liverpool have already rejected two bids – of up to £40m – from Manchester City for Sterling and Rodgers remains keen to keep the player.
Sterling is under contract with the Reds until 2017 but his relationship with the club has deteriorated since he turned down the opportunity to sign an improved deal worth £100,000 a week – a significant increase on his current wages of £35,000 – in January.
Earlier, former Liverpool captain Steven Gerrard criticised Sterling’s behaviour and told him to ‘be a man’ about his future.
In an exclusive interview with Sky Sports News HQ from new club LA Galaxy, Gerrard accused Sterling of letting down Liverpool’s supporters.
Gerrard said: “I’m not happy with all that carry-on and I don’t think there’s any need for it. They all need to be men about the situation.
“Raheem needs to go in and speak to the owners and to Brendan himself, tell them what he wants and go about it that way. You don’t have to throw illnesses in and refuse to go on tour.
“There are millions and millions of Liverpool fans around the world who are itching to see Raheem Sterling in a Liverpool kit. So I don’t think it’s fair on them if he is behaving like that.”