The Blues appeared close to sealing a deal for the Dutch international, but now he will remain in Manchester.
That's according to The Athletic, who state that Man City would have only sold their left-footed centre-back if his valuation was met.
That is something that Chelsea have clearly failed to do, which means they will now move on to other targets.
The west Londoners are close to sealing a deal for Napoli centre-back Kalidou Koulibaly for £35million.
And they are reportedly being in talks with Paris Saint-Germain's Presnel Kimpembe.
Juventus' Matthijs de Ligt and RB Leipzig's Josko Gvardiol are two other defenders they have been linked with and could pursue this summer.
Ake is heading into his third season as a City player, having signed from Bournemouth in a £41million deal, where he has made 40 appearances and won two Premier League titles.
And him staying could mean that the club will now sanction a deal for Oleksandr Zinchenko to leave the club.
Arsenal are reportedly closing in on the versatile Ukrainian, who can play at left-back or central midfield.
Man City may then increase their efforts to sign Brighton full-back Marc Cucurella who excelled on the south coast last season.