The Bosnian international was heavily linked with an exit from the Italian capital at the the start of the 2020/21 season.
However, a move away from the Stadio Olimpico failed to materialise and relations between the club and Dzeko have worsened as a result.
The former Manchester City star has still remained an important squad option for the Serie A side, with seven league goals in 15 league appearances.
But he is still rumoured to be unhappy with his situation in Italy and wants to leave the club before the winter transfer window closes in the coming days.
According to reports from Mundo Deportivo, both Real Madrid and Barcelona are monitoring the situation and could make a cut price offer if the opportunity arises.