City expect to receive a fee of between £50 million and £60m for the England winger, who has a year left on his contract at the Etihad Stadium, and if a suitable offer is made he will be allowed to move to Stamford Bridge.
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Sterling has made it clear he would be interested in a new challenge after seven years at City and has been impressed with Chelsea's plans to make him a key player under manager Thomas Tuchel.
Sterling has delayed talks over signing a new contract at City because of fears he could be sidelined in Pep Guardiola's vision for the future and the 27-year-old believes he is more likely to get regular first-team football under Tuchel.
Sources have told ESPN that City would rather Sterling moved abroad amid tentative interest from Bayern Munich, Real Madrid and Paris Saint-Germain but they will respect his wishes if he has his heart set on Chelsea.
Owner Todd Boehly has already made contact with City bosses to enquire about their valuation and sources have told ESPN an agreement could be wrapped up relatively quickly.
Even in the event of Sterling's departure, sources have told ESPN that City will remain focused on signing a left-back rather than further bolstering their attack.
Erling Haaland has already joined from Borussia Dortmund while the club have also turned down loan approaches for Julian Alvarez, who was signed from River Plate in January, to keep the Argentinian in the squad for next season.