Chelsea were keen to bring in Dzeko in January, and since the end of the campaign reports have suggested that the Bosnia-Herzegovina international could move to China.
However, Dzeko - who scored 24 goals in Serie A and Champions League fixtures last season - is only focused on another successful year at the Stadio Olimpico.
The 32-year-old told the club's official radio station: "What goals do we expect to achieve this season? In Rome we always think too much about things and I do not want to do that.
"We bought important players, but the market is not finished so we can see and there are three great competitions, many players, a coach who transmits the right mentality, the one we need here, and hopefully in the league we will do well from the beginning and win many games.
"This is the most important thing. I feel very good here, even my wife and my children are doing well. We have had an incredible season in the Champions League and we hope to do better this year."
Dzeko still has two years remaining on his contract.