It has been reported that Sunderland have made an offer of £11 million to Roma to secure the services of the former Manchester City striker this summer.
Calciomercato.com recently claimed that London side West Ham are interested in Dzeko.
Dzeko scored eight goals and created 22 chances in 31 Serie A appearances for Roma last season.
The striker had a pass accuracy of 66% and a shot accuracy of 50%, and won 100 headers, 18 dribbles and 11 tackles.
Roma finished third in Serie A during the 2015-16 campaign and have a chance of playing in the group stage of the Champions League next season.