The wantaway forward was left out of Liverpool's squad which flew out on Sunday for their pre-season tour of Thailand as talks over the big-money switch progressed.
And England international Sterling, who has been at loggerheads with Liverpool since turning down a new contract earlier this year, is now on the verge of completing his move to the Etihad Stadium.
City have already failed with two bids for Sterling, the second reported to be worth £40million, this summer, with Liverpool understood to be holding out for nearer £50million.
Assuming the 20-year-old agrees terms with City and passes a medical, his protracted and acrimonious departure from Anfield will finally be sealed.
Sterling has been at loggerheads with the Reds since February, when manager Brendan Rodgers claimed he had been offered "an incredible deal".
Two months later Sterling angered the club by confirming, in an unsanctioned interview with the BBC, that he had turned the contract down.
The impasse deepened when Sterling's agent, Aidy Ward, claimed the player would not sign even for £900,000 a week".
He became embroiled in fresh controversy after photographs emerged of him appearing to puff on a shisha pipe, and then allegedly inhaling laughing gas.
Sterling missed the start of pre-season training earlier this week, citing illness as he sat out Wednesday and Thursday's sessions before returning on Friday.
It had been reported that he had asked Rodgers if he could be excused from the pre-season tour, although he was initially named in the squad until Sunday's developments.
His actions have prompted criticism from a host of former Liverpool stars with Steven Gerrard the latest to speak out, the former Anfield skipper revealing he is" not happy with all that carry-on".
Sterling joined Liverpool from QPR's academy in 2010 and has made 129 appearances for the club, scoring 23 goals.
He made his senior England debut in 2012 and has scored one international goal in 16 appearances.
Liverpool fly to Bangkok on Sunday ahead of their first friendly against a Thai All Stars side next Tuesday.