City are still in the hunt to win four trophies in the Chilean's first season season at the helm after he was charged with the task of replacing Roberto Mancini in June.
Manchester United won the Premier League title at a canter in Alex Ferguson's final season before he retired, but David Moyes has endured a difficult start to his tenure at Old Trafford.
United are seventh in the table and although they are still in the UEFA Champions League, their form this season has not suggested they are capable of being crowned European champions.
As Pellegrini prepares his side for Tuesday night's Champions League last 16 first leg tie against Barcelona at the Etihad Stadium, the Chilean has no doubt his side have taken over as the premier club in Manchester.
And the former Real Madrid coach is determined to ensure it stays that way.
He said: "If we only consider this season, there is just one club in Manchester and it is ours,
"But you cannot forget what United has done in the previous years
"We are aiming to keep growing by winning many trophies, not just national, but international trophies.
"We are fighting for four titles this year. We have to be patient because you cannot change the team from one day to another. But we have to keep the philosophy of the style and for that you need time."
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