Discussions are at an early stage with City assessing their options as they look to add four new players this summer with defence a priority.
No bid has yet been received by Bournemouth.
Ake, who is valued around £40million, also has interest from former club Chelsea and is among the centre backs being considered by Manchester United.
The 25-year old has long been considered by City as he can cover at left back and counts as a homegrown player.
They have also discussed Kalidou Koulibaly of Napoli, Diego Carlos of Sevilla and Leicester City left back Ben Chilwell.
Talks are also ongoing with Valencia over a deal for £40m-rated Spain winger Ferran Torres, 20.
City are also continuing to invest in youth with Gremio’s highly rated 17-year old midfielder Diego Rosa a target.
The Brazil youth international could arrive for around £4.5m but would not be registered until January owing to his age.