The decision follows an improvement in Sterling's relationship with City manager Pep Guardiola, who left the 27-year-old out of the team for much of the second half of last season.
Sterling will still wait to see how much game-time he is given over the next few weeks before committing to the club he joined from Liverpool for £49million seven years ago.
But in a significant development, he has accepted for the first time that he will not leave City this month.
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