The Bosnia-Herzegovina international has not featured since coming off the bench in the 2-2 draw at QPR earlier this month and lasting only a few minutes before limping off.
Dzeko is not available for Sunday's Premier League game against second-placed Southampton, but could face either Sunderland on Wednesday or Everton three days later.
City manager Pellegrini also revealed that David Silva (knee) and Aleksandar Kolarov (calf) are not yet ready to return.
"No news about Silva, Kolarov or Dzeko – they will not be fit for this game. Everyone else is fit for this game," said the Chilean.
"I suppose Edin Dzeko will be fit next week. There are no complications with David Silva, it was a ligament injury and he is recovering."
City fought back to secure a stunning 3-2 victory over 10-man Bayern Munich in midweek courtesy of a hat-trick from Sergio Aguero.
A win at Roma next month will ensure the Premier League side progress along with Bayern, provided the Bavarian giants beat CSKA Moscow at home in their final Group E game.
Pellegrini's men also came from behind to beat Swansea City 2-1 in the Premier League last weekend and the former Malaga coach believes both victories showed there in no disharmony in his squad.
"We can't complain about our spirit. We were losing against Swansea and we scored twice – the same against Bayern," he said.
Pellegrini welcomes Yaya Toure and Fernandinho back into the squad after they missed the win over the Bundesliga champions due to suspension.
