According to The Sun, the contract is believed to be for five years and worth about 130,000-pounds-a-week and is ready to be signed in the next few days.
Kompany, 26, verbally agreed to City in the deal, as player prepare to jet out for a pre-season tour of the Far East.
He will now be at the Etihad until well into his thirties, which is being seen as a big boost for everyone at the club.
The former Hamburg defender had impressed with his leadership skills on and off the pitch since taking the armband from the controversial Carlos Tevez last summer.
The Blues are hoping that it could be a double celebration with David Silva also in talks over an improved deal. (ANI )