Manchester City hope to identify their new boss within a week and clinch his appointment before launching their pre-season programme on July 4.
Even though Chris Coleman and Mark Hughes have been linked with the club, City sources do not expect their new boss to be British.
Chief executive Alistair Mackintosh is actively leading the search for a new manager and is believed to have had talks with Ramos' advisors already.
A City source said: "There is a need now to move quickly. We could even see an announcement within the next seven days."