The Bosnia international finds himself vying for a starting berth alongside Alvaro Negredo, Stevan Jovetic and Sergio Aguero at the Etihad, and Dzeko has claimed that he welcomes the strength in depth.
"Pellegrini brought Negredo with him from Spain, which implies that he must give him a chance to show his potential," The Mirror quotes his as saying.
"There will be many matches ahead for us to fight for a position at the club.
"I don't feel threatened by Negredo. It just raises the bat in terms of competition and it's up to me to fight - and I will do so. I have never given up anything in my life so I certainly won't be giving up now."
City hammered Norwich City 7-0 on Saturday, with Dzeko adding a late strike.