The Sunday Mirror says City chairman Khaldoon Al Mubarak has stepped in to prevent the transfer from collapsing.
City were told to increase their initial offer to the Wolfsburg striker by £50,000-a-week. They were ready to pay him £120,000-a-week but Dzeko wanted £170,000-a-week.
Chairman Khaldoon rang Dzeko's advisers on New Year's Eve to resolve the dispute with the Bosnia striker.
No agreement has yet been reached but City believe a compromise can be reached and the deal will go through.