Bournemouth are looking to cash in on the Dutchman following their relegation from the Premier League and City are close to agreeing a deal worth around £40 million with a further £1m in bonuses.
Chelsea had a buy-back clause in the deal that sold Ake to Bournemouth in 2017 but sources have told ESPN they are not interested in a deal to re-sign their former player.
The 25-year-old has made 121 appearances for Bournemouth after moving from Chelsea, initially on loan, in 2016. He has won 13 caps for the Netherlands.
City have moved quickly to solve their problems at the back after agreeing a €23m deal for Valencia winger Ferran Torres. Torres is expected to be confirmed as a City player once he has undergone a medical.
Ake's impending arrival will add further doubts about the futures of Nicolas Otamendi and John Stones. The pair have fallen behind Eric Garcia in the pecking order since the restart and have been linked with moves away from the Etihad Stadium.
Sources have told ESPN that director of football Txiki Begiristain is open to adding another central defender even if Ake does arrive. Napoli's Kalidou Koulibaly, Villarreal's Pau Torres and Benfica's Ruben Dias are among the names in the frame.