The Chilean coach has promised the 27-year-old striker he will be given the chance to "show what he can do", while also revealing his gruelling pre-season fitness regime
The Bosnian striker was largely used as an impact substitute by former boss Roberto Mancini last season, but Pellegrini is adamant Dzeko will be given a chance to prove his worth.
"I spoke two weeks ago with Dzeko when he was on holiday and he does not have any problems," Pellegrini told reporters.
"He will stay here. For me, he's a very important player. I'm sure that he will give this year the performances to show what he can do."
The former Real Madrid and Malaga boss has also revealed he has his squad on a fierce fitness regime ahead of City's opening pre-season friendly against Super Sport United on Sunday.
"The most important thing at the moment is the fitness and they're working very hard with Jose Cabello [fitness coach]," he said.
"In terms of football, they're just playing small games of six or seven-a-side with one touch, but nothing more.
"I've not had a problem with them. It's logical that at the beginning they ask a lot of different things. They've worked very hard with us and they're comfortable with each other."