The Roma midfielder has been linked with a move to the Premier League champions recently, with the 23-year-old reportedly being available for a fee of £21m.
Dzeko, whose own future at the Etihad Stadium is far from certain, admits that he would choose to remain at City should they bring in Pjanic.
Asked whether City could sign Pjanic, Dzeko told Sport.ba: "I sincerely hope so.
"I have recommended Pjanic before to Manchester City - they know all about him. On one occasion, the manager, Roberto Mancini, asked me whether Pjanic was Bosnian. I said, 'Of course, he's Bosnian!' I wouldn't be surprised if Pjanic came to City, and I sincerely hope he does.
"If 'Mire' came to City then I would certainly not want to leave the Etihad."
Dzeko has been linked with a move to Arsenal and Borussia Dortmund in recent times.