The Bosnia striker has been linked with Tottenham.
Pellegrini said: "The future of Dzeko has been decided a long time ago.
"He's a top striker and a starter and he will have a high level of performance like he did all the years he played in Germany.
"I have confidence in him, and the players who came in are only support for a squad that needs to have every place doubled up with top players. So there is no problem with the future of Dzeko."