The Bosnian, who has found himself behind Sergio Aguero and Alvaro Negredo in the pecking order at the Etihad this season, has long been linked with a move to the Gunners in order to take the weight of expectation off the shoulders of Olivier Giroud.
"No, that is not the case [that Dzeko could be sold]," Manchester City manager Pellegrini told reporters.
"I put my trust in him before the season and I have just as much trust in him now. It is very important for this club to have a good squad because we have a lot of games to play from now until April and, if we want to win trophies, we need important players.
"Maybe at the moment he is not playing as much as he would like, but he remains an important part of the squad."
City travel to West Bromwich Albion on Wednesday.