City are second in the Premier League, one point behind Arsenal, and are in with a chance of completing the quadruple.
Watford visit the Etihad Stadium in the FA Cup on Saturday, while the meeting with Barcelona in the Champions League first knockout stage is in February.
When asked if he feels that City are on course to become a major force in European football, Pellegrini told The Guardian: "I think so. We are working every day more. We beat Bayern Munich already in Germany so I repeat this team has a lot of things to improve but I think we are not so far from the big teams.
"The only way to continue improving is to win titles. If you win titles it's because you do the right things.
"All the big teams have good players also. The way we are working, maybe given time we are going to be a very strong team in Europe."
Pellegrini's side have scored 106 goals in all competitions this season.