The 27-year-old has one year remaining on his City deal and has drawn attention from top foreign teams.
Sterling left Liverpool in 2015 and was acquired by City for £49 million. Since then, he has scored 131 goals in 339 appearances.
If the transaction goes through, Sterling, 77 England caps, would be Chelsea’s first significant acquisition since being acquired by a group headed by Todd Boehly this summer.
Before Chelsea departs for their preseason tour of the United States the following week, it is anticipated that the transaction will be completed in time for Sterling to join the team.
Although Sterling wanted a new challenge and was delighted by Blues boss Thomas Tuchel’s ambition and the position described to him, BBC Sport understands that all sides have reached mutual choices.
Despite Chelsea’s open and secret desire to recruit him, Sterling was enticed by interest from other top teams, including Barcelona, Real Madrid, and Bayern Munich.
Sterling has no ill will against City or manager Pep Guardiola, and the club wanted him to remain.
He sees this as the most important deal of his career and hopes to play a crucial part in a team competing for all the top awards.
The Ballon d’Or is one of the professional and team goals that Sterling still has left to accomplish.
Only John Terry and former City teammate Fernandinho have more Premier League championships than him, outside of players for Manchester United.
He has yet to claim a Champions League victory, however.
Sterling started the discussion regarding his future with City, and it is believed that he values the time granted to him to decide.
Sterling boosts Chelsea’s offensive options.
After Romelu Lukaku returned to Inter Milan on a season-long loan, Tuchel sought to strengthen his impressive lineup.
With 15 goals in all competitions, the Belgian striker led the Blues in scoring last season, just ahead of Kai Havertz (14) and Mason Mount (13).
Only Sergio Aguero (124) has scored more goals for City since Guardiola took over as manager than Sterling (120).
Sterling earned his fourth league championship and seventh major award in seven seasons with City last season after scoring 13 goals in 30 Premier League games.
But the acquisition of Jack Grealish last summer, as well as the arrival this summer of strikers Erling Haaland and Julian Alvarez at Etihad Stadium, limited his possibilities.
During both legs of Real Madrid’s elimination in the Champions League semifinals and the thrilling season-ending match against Aston Villa, Sterling sat on the sidelines.
But he did help City come back from a 2-0 deficit to win 3-2 and edge Liverpool for the league championship by setting up Ilkay Gundogan’s vital opening goal.