Dzeko and Pellegrini had a successful spell together at Manchester City, but Pellegrini has just chalked the talk down to the usual football gossip.
You can talk about five, six or seven players that are linked with us. We must not talk about one player," Pellegrini said.
"I know him well but we are not thinking about that at the moment."
The duo won the Premier League together at City, with Dzeko previously picking up another league title under Roberto Mancini. The West Ham boss went on to reveal that there have been no new injury issues over the international break.
"Marko [Arnautovic] is okay. He returned from internationals where he played just one game and worked without any problems," he added.
"We must be careful about his knee but it is ok but it allows for him to play games."