Pep Guardiola’s side re-established themselves as a dominant force in English football last season with a Premier League and Carabao Cup double.
It is, however, in Europe that City are really looking to make their mark, with big spending intended to have delivered more continental success.
The Blues have reached the semi-finals of the Champions League in the past, and are back into the last 16 for 2019, but Gundogan is aware of the need to go all the way and match the achievements of those perched at the summit of the global game.
The German playmaker told UEFA’s official website ahead of a meeting with Schalke on Wednesday: “We've experienced a lot in the Champions League in recent years – not all of it positive, of course. We should've won it at least once.
“Every club, every team, every single player would like to lift this trophy sometime. The competition to win it is so big year in, year out, so your chances are not that good, but there's a team that wins it every year.
“If you want to be in the international elite, as a club and as a player, you need to clinch this trophy.
“If we were to win it someday, the club would enter a new era – the same level as Real, Barca, Bayern [Munich] or Juventus. Our job is to try to give it our all to make that a reality.”
Gundogan added on a meeting with Schalke, a club that helped to put him on the path to stardom after joining the youth ranks in his native Gelsenkirchen: “We are clear favourites in this tie and rightly so.
“However, every team in the last 16 has earned the right to be there. Because of that, we'll respect our opponents and prepare for it as if it's a final because it's the knockout phase and every mistake can be severely punished.”