Citing reports from Italy, the Mirror claims Inter Milan are targeting the Bosnian international to spearhead their new-look squad heading into the second half of the season.
It's been a difficult 12 months for the Italian giants, but with a change of ownership and management, the club hopes to return to former glories in the near future.
They currently sit fourth in Serie A, having finished ninth last term, and new owner Erick Thohir is thought to be ready to hand Inter boss Walter Mazzarri a significant transfer kitty for the January transfer window.
And Dzeko, who has reportedly been told he can look for a new club, is thought to be high on their shopping list.
Arsenal and Borussia Dortmund have both been linked with the frontman, with the Gunners expected to move for a new striker in the winter window.
Arsene Wenger wants to improve his attacking options, with France international Olivier Giroud the club's only Champions League-quality forward.
Back-up Nicklas Bendtner has failed to make his case for regular inclusion in the Arsenal starting eleven, and Wenger has been linked with a number of big-name targets, including Dzeko and Real Madrid forward Karim Benzema.
They face competition for Dzeko however, with the Daily Mirror suggesting Inter Milan are already putting together a package to bring the Bosnian forward to the San Siro.