Having continued to spend big over recent years, the ambition of those at the Etihad Stadium is to complement domestic successes with a European triumph.
City made it as far as the semi-final stage in 2015-16, but have crashed out at the last-16 in three of the last four seasons.
Pep Guardiola’s side were, however, to get off to a winning start in the current campaign on Wednesday, as they eased past Feyenoord 4-0, and Stones believes their sights should be locked on chasing down major silverware.
The England international told CityTV: “We’ve got a dream and we have to feel confident that we can do it. Why not?
“We want to be in every competition, trying to win things.
“We’ll take things game by game and see where it takes us. It’s a great start; hopefully, we can take it into the next game.”
Stones played a leading role in the commanding victory on Dutch soil, as he bagged a brace and helped to keep a clean sheet.
The 23-year-old is delighted to be playing his part in City’s trophy quest, with Guardiola having assembled a star-studded squad which is being widely tipped to challenge at home and abroad.
“It was brilliant,” Stones added.
“Getting an early goal always helps. We controlled the game.
“To come away from home in the Champions League, score four goals and keep a clean sheet is a massive boost for us to take into the next game.
“I’ve never scored twice in a game, apart from probably when I was about seven!
“Kevin De Bruyne put it on a plate for me though – I couldn’t really miss! That’s one of Kev’s great strengths – his deliveries; both in the air and on the floor. We just have to keep getting on the end of them.
“I’m pleased with scoring and keeping a clean sheet – that’s pleasing for us defenders!”