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.
The French outfit Paris Saint-Germain are reportedly weighing up a summer move for Roma midfielder Miralem Pjanic, according to Gazzetta dello Sport.
The Ligue 1 champions, who successfully booked their place in the quarter-finals of the UEFA Champions League on Wednesday, are once again expected to make a big move at the end of the season.
Manchester United have reportedly joined the race to sign Stoke’s Asmir Begovic as a potential replacement for David De Gea.
— Sky Sports Football (@SkyFootball) July 6, 2015
Bayer Leverkusen defender Emir Spahic has extended his stay at the BayArena by signing a new one-year contract with the club.
— Bayer 04 Leverkusen (@bayer04fussball) November 7, 2014