According to the TV channel, the two parties remaing "poles apart" on the player's wages and with the World Cup around the corner, talks have been frozen and no new negotiations are planned. They have met twice since May 6 but have made no ground on reaching a deal.
The 23-year-old, now at the World Cup with England, earns £175,000-a-week and has two years left to run on his contract. However, after two meetings between the club and Sterling's representatives since the end of the season last month, no new contract has been agreed. Sterling, meanwhile, pockets £175,000 per week.
Sterling arrived from Liverpool for a then record fee of £44m in 2015.
City's Belgian maestro is reported to get £350,000 each week and is one of the Premier League's top earners as a result.
With England's first game less than a week away, Sterling knows a successful World Cup campaign - and some key performances on the biggest stage - will go a long way towards loosening City's purse strings and simultaneously alerting some of Europe's top clubs.
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 Russian Federation today it now appears that further negotiations will have to wait.
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