The Blues’ only silverware in Europe came in 1970 with a European Cup Winners’ Cup success.
Since then, the 2016 Champions League semi-final has been the Club’s best showing in Europe’s premier club competition - but he says the Blues' confidence is growing year on year.
"It's one thing for us to make a statement about being this or that, but for us to go out and do it, as in previous years we’ve felt how difficult it is,” said Kompany.
“We are trying to break into a well-established order - Barcelona, Bayern, Real Madrid - any team who has tried it has failed.
“First, it's FC Basel then getting to the stage where we can measure ourselves against these teams and feel like we can beat them."
Kompany added the Blues are still on a learning curve in the Champions League but believes each season the quest to land the trophy gathers momentum.
He said: “There is a lack of experience for sure and we've been caught out on occasions when we shouldn't have, but things have changed and 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.”
And the captain also said thoughts of winning four trophies this season are for others to have - not the players, who are only focused on a game-by-game basis.
"Have we thought about it? No - not at all, I can honestly say, the key thing I've noticed - I can't say if it will get us all the trophies - is the ability to switch back on for every game, motivation, respect for opponents, to make sure we are 100%.
“I've not experienced it in any team I've been in before. Quadruple talk - there's been none - but winning the next game and the next one, always.
“I don't really make a distinction between Champions League, the Premier League, the FA Cup or the Carabao Cup - we just have to win the game we are playing. It's a balance between not under-estimating the smaller teams and not over-estimating the bigger teams.
“From game to game, I’ve never experienced this kind of focus, intensity and motivation.
“But we’ll be judged by the trophies we win and in terms of achievements, we have nothing as yet."