Kompany believes City can build on their Premier League success and must now start to think about challenging for European glory.
"I'm happy in Manchester. Lots of people want me to talk about moving but what interests me is Manchester City," he said in The People.
"The project here is not just a sporting one. It will bring a lot to the city and to the people.
"We can't stop with the title. We want to win the Champions League.
"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."