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The 23-year-old has a contract through the end of next season, but Pep Guardiola has been keen to lock him up for the long-term.
Sterling recently made his 200th Premier League appearance, and has 53 goals and 52 assists including 35 and 31 over 105 league apps for City.
Overall, the England international has 48 goals and 52 assists for City.
Sterling had been mentioned as a possible Real Madrid target, and the reported new deal would represent a victory for Guardiola (not that anyone’s begging to leave City, anyway).