The 25-year-old scored 11 goals and registered 10 assists in 47 appearances across all competitions during the 2020-21 campaign.
However, the Italy international has now entered the final year of his contract with the Serie A outfit, and the likes of Liverpool and Barcelona have been credited with an interest.
The 23-year-old who plays for Leicester City, on loan from Roma, has struggled to become a consistent part of Brendan Rodgers’s plans this season.
The Turkey international has been a regular in the Europa League, but the midfielder has made a mere nine appearances in the English top flight.
The 35-year-old will see his contract at the Stadio Olimpico expire at the end of next season.
Dzeko has scored 117 goals and made 52 assists in 253 appearances for Giallorossi since arriving from Manchester City in 2015.
The league leaders Inter Milan had been linked with the potential signing of the frontman during the January transfer window.
Arsenal midfielder Henrikh Mkhitaryan is on the brink of joining the Italian outfit AS Roma on a season-long loan with Giallorossi trying to wrap up the deal before Monday’s deadline.
According to Gianluca Di Marzio, Roma are trying hard to bring in the 30-year-old midfielder over the next 24 hours.