The Belgium international says the Citizens are committed to winning major trophies in the future and has no intention of missing out on that success
City won their first league title in 44 years this season, adding to an FA Cup final victory in the previous campaign.
And Kompany says there is still much more to come from the Abu Dhabi financed club, as they look to add European success to their domestic wins.
"We can't stop with the title. We want to win the Champions League," the Belgian told The People.
"Is it possible in three to four years? Maybe not, but when I see what's been achieved at the club in the last few years, nothing is impossible."
Kompany was bought to the club by previous manager Mark Hughes, and gone on to establish himself as arguably one of the best central defenders in Europe.
However, the 26-year-old says he has no interest in leaving the Etihad Stadium, and is focused on the long-term project that City’s owners are bringing to Manchester.
"I'm happy in Manchester. Lots of people want me to talk about moving but what interests me is Manchester City," he added.
"The project here is not just a sporting one. It will bring a lot to the city and to the people.”
After being dubbed 'noisy neighbours' by Manchester United manager Sir Alex Ferguson, City are emerging from the shadow of their illustrious rivals, and it’s something that Kompany hopes to continue for the foreseeable future.
He explained: "It's not a three-year project but rather one for 10, 15, 20 years. It's exciting to think I can be part of taking the club where it wants to go.
"The project is to take the club back to its former glories but people won't see this for perhaps another 10 years. I'm happy to be part of all that."