According to sources, City expect to receive a fee of £47.5 million rising to £50m in add-ons for Sterling. The winger is keen on a new challenge and has been impressed with Chelsea's plans to make him a key player under manager Thomas Tuchel.
The 27-year-old confirmed on Wednesday that he will end his seven-year stay in Manchester this summer.
"Seven seasons, 11 major trophies, a lifetime of memories," he wrote on social media. "To the coaching staff who have played a massive role in my development over the years. To my teammates who have become more than just those I share a pitch with. To the backroom staff, to the office staff, to the fans who have tirelessly supported the team. And to everyone involved with Manchester City, my respect for you couldn't be greater. What a ride it's been.
"I am thankful for the ups and the downs, as it's the downs that have, at times, tested my strength and resolve, and enabled me to stand here in front of you as the best possible version of myself.
"I arrived in Manchester a 20-year-old. Today, I leave as a man. Thank you for your endless support. It's been an honour to wear the shirt of Manchester City."
Sterling joined City from Liverpool in 2015 and went on to win four Premier League titles, an FA Cup and four League Cups.