Chelsea are understood to be confident of reaching an agreement for Sterling, who is set to be available for a cut-price fee with 12 months left on his current deal.
Striker Gabriel Jesus was also in the final year of his contract at the Etihad Stadium and eventually joined Arsenal in a £45 million ($55m) deal.
Sterling is understood to have spoken to Chelsea manager Thomas Tuchel and wants to play for the German, who led his side to victory over City in the 2021 Champions League.
Why does Sterling want to move?
Signed from Liverpool in a £49m deal in 2015, Sterling has made 337 appearances for City and scored 131 goals.
But with the 2022 World Cup in Qatar at the end of the year, the England international is understood to want more game time after slipping down the pecking order under Pep Guardiola.
He was left out of the starting line-up for a number of big games last season, including both Champions League semi-final legs against Real Madrid and the final day victory over Aston Villa.
The arrival of new signings Erling Haaland and Julian Alvarez plus the form of Phil Foden, Jack Grealish and Riyad Mahrez is set to make competition for starting places even more fierce. Young players such as Cole Palmer could further cloud the picture.
Will Sterling fit into Tuchel’s team?
Sterling is one of the good wingers in the English premier league. He sometimes play as a center forward and can also be used as wing back. In a 4-3-3 set up, Sterling can play in either positions in the upfront. He will also be important in a 3 back formation
What will He add to the Chelsea team?
He is one of the few players to score 100+ premier league goals and a month Messi and Aguero to score 100+ goals for Pep Gaudiola. Though he misses a lot of chances as seen by a lot of football fans, Sterling is clinical. His pace and dribbling will be useful in the team. He is the player with most penalty won the league
What else have Man City done this transfer window?
In addition to the Haaland and Alvarez moves, which will completely reshape their attack, Pep Guardiola’s club have signed midfielder Kalvin Phillips from Leeds United as a replacement for the departing Fernandinho.
Manchester City are also interested in bringing in another left-back before the end of the summer.