The 20-year-old midfielder has already attracted attention from the Premier League, with relegation-threatened Reading showing interest in the player last summer.
Now, Citizens boss Roberto Mancini has entered the race for the France youth international's signature, and is ready to make a lucrative offer in order to bring him to the Etihad Stadium at the end of the campaign.
Kondogbia has scored one goal in 19 La Liga appearances for Sevilla in 2012/13, in what is turning out to be an impressive debut season in Spain for the former Lens star.
An offer of €20million is thought to be enough to secure Kondogbia's services, with Manchester City ready to splash the cash this summer, in an attempt to close the gap between themselves and local rivals Manchester United.
Sir Alex Ferguson's side hold a 12-point advantage in this year's Premier League title race, and barring a major disaster, will likely reclaim the domestic crown.
Manchester City will be ready to come out fighting again next season, though, and according to the Daily Express have also shown interest in Kondogbia's team-mate Jesus Navas, as they look to steal a march on their rivals.