Sterling enjoyed the best season of his career to help City to the Premier League title last term, scoring 23 goals in 46 appearances across all competitions, including 18 in 33 league outings.
The 23-year-old's form had prompted City to open talks over a new deal, but Sky Sports News reports that the two parties have failed to come to an agreement over wages.
It was hoped that a deal could be agreed before England get their World Cup campaign underway against Tunisia on June 18, but with Sterling flying out to Russia today it now appears that further negotiations will have to wait.
A new four-year deal stretching to 2022 was thought to be on the table for Sterling, but despite his representatives meeting with City twice since the end of the season, they remain some way apart on an improved salary.
The report goes on to say that no fresh negotiations are planned at this stage.