Earlier this week, it was claimed that the Premier League champions and the Blues had effectively agreed terms over the transfer of the Netherlands international.
Chelsea head coach Thomas Tuchel is known to be a long-term admirer of the 27-year-old, who also played 17 games for Chelsea at the start of his career.
With Kalidou Koulibaly on the brink of arriving from Napoli and Chelsea interested in Paris Saint-Germain's Presnel Kimpembe, it appeared that the West Londoners were closing in on their three desired defensive targets.
However, according to The Athletic, Ake will now be remaining at the Etihad Stadium for at least another season.
In contrast to the claims which emerged several days ago, the report says that Chelsea never met City's valuation, something which was a significant stumbling block with Pep Guardiola not wanting to part ways with the player.
With just three other centre-backs at his disposal, Guardiola would have been required to find a replacement for the Netherlands international, who also brings versatility to the squad.
Despite the prospect of returning to Stamford Bridge, it is added that Ake is happy to be spending a third campaign at the Etihad Stadium.
The player has made just 40 appearances in his first two years at City, a combination of injuries and being down the pecking order restricting his game time.
Earlier in the summer, however, Ake signalled his intent to fight for his place, saying: "Last season (2020-21) was very unhappy due to injuries, I don't really count that year. This season (2021-22) I was really 100% present and I played more. You notice an improvement in yourself, how you play. I felt good.
"I will go into the [new] season with that intention (to play for Man City). I will do everything I can to play even more."
Had City allowed Ake to sign for Chelsea, he would have been joining Raheem Sterling who has already made the switch to last season's third-placed team.
Over the past 24 hours, reports have indicated that fellow versatile player Oleksandr Zinchenko could be leaving City over the coming weeks.
Zinchenko, who like Ake can play at left-back and in central midfield, is being strongly linked with a transfer to Arsenal.