The Sunday Mirror says Dzeko is set to be offered the chance to follow Mario Balotelli out of Manchester City by Borussia Dortmund.
Dortmund are prepared to give 26-year-old Dzeko the chance to return to Germany, where he was a big hit with Wolfsburg.
Dortmund expect to lose star striker Robert Lewandowski at the end of the season and are already lining up high-profile potential replacements.
Sources in Germany claim Dzeko is at the top of boss Jurgen Klopp’s list, even though he will have to take a heavy cut to his £120,000-a-week wages.
Arsenal have also shown an interest in Dzeko, but it would suit the Blues to sell him abroad rather than let the Bosnia international join a Premier League rival.