The seventh-placed Red Devils head into the game 12 points behind their neighbours, having played two games more in an inconsistent first season under David Moyes, but have recorded two wins in a row against Olympiakos and West Ham.
The Manchester derby is the first of City's three games in hand on Premier League leaders Chelsea, whom they trail by six points, and Pellegrini knows that his side must stay focused despite United's "difficult" campaign to date.
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"The players are very motivated to try and win the title; it was a very close Premier League from the beginning of the season.
"We are now just focusing on the Premier League. Physically and mentally we are focused on trying to win the title.
"Our target is to add three points but we don't just need to win [on Tuesday] but [also] the next games until the end of the season."
City will once again be without striker Sergio Aguero due to a hamstring injury, while Matija Nastasic is not ready to return following a knee problem.
However, captain Vincent Kompany is set to play at Old Trafford after serving a one-match suspension.