City face a potentially pivotal week in their season, with Saturday's game being followed by a Champions League last-16 second leg match against Dynamo Kiev and a domestic derby clash with Manchester United.
City, who have a game in hand over all their fellow title chasers, are currently 10 points adrift of leaders Leicester City with 10 matches of their league campaign remaining.
Yet with Leicester being novices when it comes to handling a title run-in and rivals Tottenham Hotspur and Arsenal stumbling in recent weeks, the City manager feels his side have a chance to exert some pressure at the summit.
"It is a very important week," Pellegrini, who is leaving City to be replaced by Pep Guardiola at the end of the season, told reporters on Friday.
"If we win the two league games, the pressure will be on the other teams. Reaching the Champions League quarter-final for the first time would be an important achievement. I hope we will do it."
The City manager, however, will be without powerful midfielder Yaya Toure for the game at Norwich.
The Ivorian has a heel problem, and Pellegrini said he was unsure whether he would be fit to return for Tuesday's clash against Kiev, where City will take a 3-1 first-leg advantage into the game at the Etihad Stadium.
City's Argentine striker Sergio Aguero said this week that he would quit the club when his contract expires after the 2018 World Cup in order to return to his homeland and play for Independiente.
Pellegrini, however, sought to allay fan fears and said the 27-year-old could yet decide to stay on at the club.
“It’s difficult to talk about what will happen in two or three years more because players change their minds," Pellegrini said.
“Maybe he can be happy to return to Argentina -- but Kun (Aguero) has a lot more years here in Europe.”
(Reporting by Toby Davis; Editing by Hugh Lawson)
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