The striker hopes he will be joined at the Etihad next season by Pjanic.
Dzeko told sport.ba: "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.
"I sincerely hope that Pjanic will join City. 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!'"