The new City boss will take charge of his team for the first time on Sunday when they face Supersport United in Pretoria.
Speaking before the game, the Chilean confirmed that more transfer activity was in the offing following the arrivals of Fernandinho and Jesus Navas.
"We will sign maybe two or three more players," said Pellegrini.
City continue to be linked with a host of strikers. Sevilla's Alvaro Negredo and Fiorentina's Stevan Jovetic are the main names in the frame, while there has even been rumoured interest in Paris Saint-Germain superstar Zlatan Ibrahimovic.
The transfer talk has led to speculation that Dzeko could be on his way out of the Etihad, but Pellegrini insists that he wants the Bosnian to stay.
"I spoke with Dzeko while he was on holiday," Pellegrini added." He doesn't have any problem. He'll stay.
"For me, he's a very important player and I'm sure that he will give, this season, the performances we know he can."
The 27-year-old was City's top scorer in the Premier League last season, weighing in with 14 goals in 32 appearances.