The 27-year-old England international has reportedly given the club his approval to join, and the Blues have designated him as their top transfer target.
Chelsea and City still need to agree on a transfer fee, but Fabrizio Romano claims that encouraging discussions took place on Friday. The Blues will meet directly to conclude the deal.
With 17 goals and 9 assists from 47 games, Sterling enjoyed another strong season for City. He could only present for a little more than 65 minutes each time.
Given the dearth of creativity in the final third last season, it is not surprising that Sterling has been ready to join Chelsea and manager Thomas Tuchel.
Although several goals were scored, no one in the league truly distinguished out. Mason Mount led all scorers with 11, followed by Kai Havertz and Romelu Lukaku (8).