The Citizens are currently competing in Europe's elite competition for the fourth time in their history, but are yet to progress beyond the round of 16 stage of the tournament.
However, Pellegrini is adamant that his side have the ambition and talent to become multiple winners of the competition.
He told reporters: "I am absolutely sure that Manchester City will eventually win the Champions League.
"Of course, it is the most important title to win, but when it happens – and it will – it will not mean that this project is finished. City don't just want to win the Champions League once.
"The owners are aiming to become one of those clubs that believes they can win it every year. That means reaching the final or the semi-final regularly - and also winning trophies like the Premier League, the FA Cup and the Capital One Cup."
City face Roma in their second Champions League match of the season on Tuesday.