The Premier League champion's captain is seen as a potential future executive at the club and he is close to signing a new five-year deal to keep him at the Etihad Stadium.
The Belgian defender is currently under contract until 2017 but the Premier League champion has proposed an extension that will now run until 2019, which would take the City skipper up to the age of 33.
Kompany earns around 140,000 pounds a week and has previously been a top target for Barcelona.
The player has already indicated that he is happy to stay and the club's top brass see him as a possible future executive at the end of his playing days.
Kompany played 28 games for Manuel Pellegrini's side in 2013-14 as it recaptured the Premier League title.