Despite failing to find the net, the 27-year old put in a man of the match display in City's opening 4-0 win over Newcastle United following a frustrating time during the last campaign.
Pellegrini boosted his striking options during the summer by signing Stevan Jovetic and Alvaro Negredo, but he says that Dzeko can still lead the line for City if he starts scoring.
"I told him that if he wants to stay here we must see the player Manchester City bought two years ago," Pellegrini is quoted in The Sunday People.
"Dzeko played well against Newcastle - not very, very well because he must score. He worked for the team and had bad luck, and there were some good saves.
"I am confident he will score goals, of course, because he's scored goals in his whole career. We have other good strikers so we should be in very good shape.
"I don't expect a certain amount of goals from him, or any of them. It's important the team wins, who scores the goals is not important."