The future of the Real Madrid defender is still unresolved.
English media say City are looking to transfer an experienced defender to their defense.
According to ESPN, Manchester City is expected to offer him a two-year contract, with very good financial conditions.
The Premier League champions hope to secure the 35-year-old’s services if he does not reach a renewal deal with the Santiago Bernabeu squad.
Ramos’s current contract at Madrid is expected to expire at the end of June and he has just turned down a one-year renewal offered by the Los Blancos squad.