The 32-year-old club captain celebrated ten years at the Etihad last week after his arrival for just £6million from Hamburg in 2008.
The Belgium defender is out of contract next summer, with talks on the back-burner as Pep Guardiola focuses on another Premier League title.
But City are not concerned about Kompany wanting to play for another English club, and will wait before thrashing out fresh terms.
There are still worries over his long-term injuries problems, but he is still seen as a vital leader of the squad, both on and off the pitch.
It is understood Kompany is willing to take a hefty cut on his £200,000-a-week wages and agree a new rolling 12-month extension.
An Etihad source said: “There are no issues with Vinnie and everything is expected to happen when the season ends.
“There are no talks but that isn't a problem at this stage. It's going to be a similar situation to when Gary Neville was at United.
“He isn't going anywhere, we know that. His injuries have been an issue but we know he has no intentions of hanging up his boots just yet.”
Kompany is now due a testimonial at City for his service to the club, but that is not expected to happen until after he retires.
It is thought he will also take up an executive role with the City Football Group when his playing days are over.
Last year, the ex-Anderlecht ace graduated with a Masters of Business Administration degree in Manchester, finishing with a merit grade.
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