Dzeko in action for Roma in the Champions League
The Bosnian has enjoyed another impressive season for Roma in Serie A this term bagging 24 goals in 47 appearances.
Dzeko came close to joining Chelsea in January with Alvaro Morata failing to impress during his first season at Stamford Bridge.
His future in the Italian capital remains unclear and, according to Tuttosport, AC Milan are ready to capitalise on the uncertainty.
Milan believe they can prize Dzeko away from Roma with a lucrative deal this summer and in the process see off any lingering interest from Chelsea.