The French right-back’s future at the Emirates Stadium has been the subject of much doubt for some time, with negotiations to extend his contract – which expires this summer – having been fruitless for a while.
Sagna is said to be holding out for £100,000-per-week, which Arsenal have now told him he will not receive from them.
This has allowed City to enter the battle, with the reigning Premier League champions more open to bowing to his desires.
Once the season officially ends – which it will for the Gunners after Saturday’s cup final against Hull – Sagna will be able to discuss deals with other English teams, which could see an agreement reached quickly with the Sky Blues.
City chief Manuel Pellegrini is thought to be attracted to the 31-year-old’s vast experience of the English game, and may opt to push commanding right-sided defender Pablo Zabaleta to the opposite flank in order to accommodate him for next season’s title push.