Aguero limped out of City's 6-3 victory over Arsenal last weekend with a calf injury and could be missing for two months.
Dzeko joined City three years ago from Wolfsburg in a £27million deal but has been used mostly as a substitute in the Barclays Premier League over the past two seasons.
Manager Manuel Pellegrini has preferred summer signing Alvaro Negredo as a partner for Aguero, but the absence of the 19-goal top scorer means Dzeko is likely to get his chance.
The Bosnia international netted twice in City's 3-1 victory over Leicester in the quarter-finals of the Capital One Cup on Tuesday, taking his tally for the club this season to nine.
Dzeko told several national newspapers: "Sergio has had an amazing season, scoring a lot of goals, and he is an important player for us.
"That's life, and now we have to try to play games without him, and try to win. This is very bad for the team but there are a lot of players who want to play.
"I am happy to score two - that's my job. I hope it means I am back among the goals. When I'm playing, I'm trying always to score goals.
"I am a striker that has scored goals all my life, and I love to do it. When I get a chance I try to do my best. We have a superb squad and recently have scored a lot of goals."
City's victory over Arsenal moved them to within three points of the Premier League leaders ahead of Saturday's trip to Fulham.