The North-West outfit have never reached the final of the elite competition, with their best finish being the semi-finals, when they were beaten by Real Madrid in 2016.
Under Pep Guardiola in the current campaign, the team have suffered defeat just twice in all competitions, and their next challenge is a last-16 first-leg tie against Basel on Tuesday.
"Things have changed," Kompany told reporters during City's pre-match press conference. "If there is a year, a moment when the club is ready to feel at home, then it's now.
"I'm not going to say it's a matter of time - some clubs never win it - but if every year we can go with this kind of confidence, then if not this year or next year, eventually we'll get there. I'm sure of it.
"In previous years we've felt how difficult it is. We are trying to break into a well established order - Barcelona, Bayern, Real Madrid. Any team who has tried it over the last 10 years has failed.
"First, it's Basel, then getting to the stage where we can measure ourselves against these teams and feel like we can beat them."
Injury-plagued Kompany has not played in the Champions League since the semi-final in 2016.