Returning to Liverpool training on Monday, the Manchester City transfer target is believed to have reaffirmed his desire to leave the Merseyside club and asked manager Brendan Rodgers to omit him from the touring party.
Liverpool embarks on a 13-day tour on Sunday, which includes matches against A-League teams Brisbane Roar on Friday 17 July and Adelaide United on Monday 20 July.
The relationship between Sterling and the club deteriorated rapidly after the player's refusal of a £100,000 ($208,000) per week deal in April, with the player alleging the club showed him a lack of respect.
Manchester City has had two bids rejected for Sterling, for whom Liverpool is demanding a £50 million ($104 million) transfer fee.
The clubs have not been in contact since the second bid was rejected last month, although a fresh approach is expected soon.
Meanwhile, Rodgers hopes to add Aston Villa striker Christian Benteke to his Reds squad before the start of the campaign, irrespective of whether Sterling stays or goes.
