The Blues skipper, who celebrated his ten-year anniversary at the Club in August, has lifted nine domestic trophies since donning sky blue.
Having played in each of our Champions League campaigns, since City first qualified at the end of the 2010/11 season, Kompany hopes to lead his side to success in the continent’s elite competition but admits the feat is a difficult one to accomplish.
“I’d love to win a European trophy with City,” he told press, “but I’m realistic and it’s so tough.
“Across Europe, there are six or seven other teams that are thinking the same. It’s difficult because there are good teams in the Champions League. The season before last, we went all the way to the semi-final.
“We have to deal with the fact that we lost to Lyon before we think of winning the competition.
GALLERY: Open training | De Bruyne is back!
“I don’t know if you can speak in those terms (of rubber-stamping elite status). It’s the last step we haven’t achieved yet.
“Every single year that you lose, you just have to start again but we don’t want to think about the past – we just have to play at our level. You can’t ask for much more than that.
“It’s such a difficult competition to win and it takes time. I don’t want to put pressure on Pep Guardiola but we will do our best.”
Kompany signed for City from Hamburg and added his is looking forward to returning to Germany.
The defender has locked horns with Hoffenheim before and has warned against complacency.
“Time goes fast,” he declared. “Back then, Hoffenheim were in a lower league but we have seen the rise of the team, including how they played against Liverpool.
“We lost our first game (in Group F) and we can’t underestimate other teams.”
With Kompany’s compatriot Kevin De Bruyne back in training on Monday, City received a timely boost ahead of Tuesday’s clash.
Although the Belgian playmaker will not be involved, the skipper admitted his will be a welcome return to action.
“It’s difficult to quantify how much of a loss (he has been),” he reflected. “He is one of the best midfielders.
“We get more goals and assists with him but luckily, we have a huge squad and we have the players to fill the gap.
“He has a huge presence and you don’t find it anywhere else in football.”
Kompany has not featured in Guardiola’s starting XI since August but insists he is patiently waiting his turn, ready to be called upon when needed.
“I’m a proud man but I’m rational and patient,” he stated. “I’ve been lucky to have played in most of the games, even when coming back from injury.
“I got back pretty quickly but you take someone else’s space – so I look at players who play in the right way.
“When I play, I’m happy but when I don’t, I’m the first to help players.
“I’ve still got training to prove myself to the manager!” he joked.
“I’m a player of this wonderful Club and I have the same duty of every other player – that’s to play my best until the last day of my contract.”