Express Sport understands the Bosnia international is set to sign for Bournemouth in a £10million deal within the next 24 hours.
The Chelsea shot-stopper joined from Stoke in the summer of 2015 after proving his quality in the Premier League.
But Begovic has struggled for game time since his arrival due to first choice Thibaut Courtois.
Antonio Conte has continued to restrict the 29-year-old to appearances in cup competitions with Courtois playing an important role in Chelsea’s title bid.
Thibaut Courtois has been favoured to Asmir Begovic at Chelsea during the past two seasons
Ultimately I didn't get as many games as I would have liked
As a result, Begovic is ready to quit, and accepts his situation has been difficult to manage for Conte due to Chelsea’s talented goalkeeping department.
“Of course [I thought I could compete], because chances to play for Chelsea don't come around every day and top clubs like this in general,” Begovic said.
“When they (transfer to a big club like Chelsea) come around, if you don't believe in yourself and don't think things can happen for yourself, then you shouldn't be in this game.
“I truly believed there was a chance and something could happen, and ultimately I didn't get as many games as I would have liked.
Antonio Conte has stuck with Thibaut Courtois during Chelsea's push for the Premier league title
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GK: Asmir Begovic – 7: Made some great saves for a deserved clean sheet
Asmir Begovic is expected to have made his last Chelsea appearance against Brentford
“Thibaut is on absolute fire this year and is one of the best goalkeepers in the world, I knew that, and I wanted to test myself against those guys.
“I feel like I am one of them but unfortunately no club is big enough to have two really good goalkeepers.”
Begovic started in Chelsea’s 4-0 FA Cup fourth round win over Brentford on Saturday, and that is expected to have been his farewell appearance.
The ex-Portsmouth man is opting to prioritise game time over winning medals from the bench in west London.