City need to overturn a first-leg deficit against Tottenham in the Champions League on Wednesday to keep their bid for an unprecedented clean sweep of trophies alive.
City trail 1-0 on aggregate midway through the quarter-final tie after defeat in London last week.
Stones said: "I don't think a lot of things are impossible, that is the mindset of different people.
"If you don't dream big then you are not going to get anywhere near it. It comes from within everyone, we have this belief and ambition to do it."
City are also involved in a close battle for the Premier League title with Liverpool. Stones is confident City can hit their stride in the run-in.
He said: "These sorts of games bring out the best in us. We have to trust in ourselves and our team-mates and perform on whatever day we have a game.
"We have five games left, everything to play for and we have to enjoy the pressure and roll with it and believe in ourselves."
Manager Pep Guardiola is relishing the challenge ahead of City as they continue to push for glory on all fronts.
Guardiola said: "I know how difficult our fixtures are and we play Tottenham and then the derby at Old Trafford and Burnley.
"All the games are tough. We don't have rest. We play nine, ten or 11 games more than Liverpool and I love this challenge."
Guardiola feels the fans, as well as the players, have an important part to play on Wednesday.
He said said: "I want to see that they want to get to the semi-finals, not just the players, the fans too. I want to see that."
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