The striker has started nine of his 14 appearances in all competitions this season and is being tracked by a host of European clubs including Borussia Dortmund, Inter and Roma
Goal exclusively revealed in November that the club will not offer the Bosnian a new deal and are willing to listen to offers for the 27-year-old.
Dzeko, a €33 million signing from Wolfsburg in January 2011, has started just nine games under Pellegrini this season and has scored seven goals in all competitions.
With Arsenal targeting a striker in January, Dzeko is also being monitored by a host of European clubs including Borussia Dortmund, Inter and Roma.
"No, that is not the case [that Dzeko will be sold]," Pellegrini told the Daily Telegraph.
"I put my trust in him before the season and I have just as much trust in him now. It is very important for this club to have a good squad because we have a lot of games to play from now until April and, if we want to win trophies, we need important players.
"Maybe at the moment he is not playing as much as he would like, but he remains an important part of the squad."