The former Manchester City man has been subject to rumours linking him with a return to the Premier League in the future.
Dzeko left the Etihad for Roma initially on a one-year loan deal before making the deal permanent during the 2015-2016 season and he has gone on to become the club’s marksman guiding the Serie A side to the Champions League semi-final last season.
The Bosnia and Herzegovina striker has been linked with a move to the Premier League and with West Ham but the Hammers boss has dismissed such rumours.
The former Manchester City manager has denied speculations suggesting West Ham could make a January move for the striker who played under him at the Etihad.
Speaking on a potential return to the English first division in the future Dzeko said:
“Regarding the Premier League, maybe it’s too late, you never know.”
Speaking in a news conference on Thursday, Pellegrini when posed with the question of collaborating with his former player at West Ham suggested he was not on the club’s radar.
“You can talk about five, six or seven players that are linked with us,” Pellegrini told reporters.
“We must not talk about one player. I know him well but we are not thinking about that at the moment.”
The Chilean manager went on to confirm that Marko Arnautovic would be available for the London derby when West Ham host Tottenham on Saturday.
He also acknowledged the threat Harry Kane and Spurs pose to his side on Saturday and labelled the striker as “one of the world’s best”.
“He’s okay,” the Chilean continued. “He played just one game [for Austria in the international break].
“He has worked with the squad without any problems. He must be careful with his knee.
“Harry Kane is one of the best players in the Premier League, maybe the world,” Pellegrini added. “They have a lot of international players, they have a complete squad.”