City are not planning to bring in any fresh faces in the January transfer window, with Pellegrini happy his side are strong enough to land the title.
Arsenal are keen to add firepower to boost their title bid and are among a number of clubs interested in Bosnian Dzeko (below).
Dzeko, 27, has struggled for first-team chances behind Sergio Aguero and Alvaro Negredo in the pecking order at the Etihad Stadium.
But he has still managed to net 10 goals so far this season and with Aguero currently sidelined with a calf injury, Pellegrini needs the former Wolfsburg striker.
He said: "There was never any chance of Dzeko going in January.
"He is a very important member of the squad.“There was never any chance of Dzeko going in January”Maneul Pellegrini
"If you revise the last month you will see that he has played games in December and he will be very important.
"Every player wants to play every game.
"I repeat that I think he is happy. He is an important player and there may be offers but he won't leave."
Rodwell, 22, has started just one Premier League game under Pellegrini - back in September against Stoke.
But Pellegrini has dismissed any chance of the England midfielder leaving.
He said: "At this moment nobody will be leaving the club."