The Citizens managed to close the gap to leaders United to five points following their 2-0 win over Fulham and the Red Devils’ 1-1 draw with Tottenham at the weekend.
And the striker believes Roberto Mancini’s men are on course to continue narrowing the deficit with 15 games left to play this season.
“We have to just keep doing what we’re doing,” Dzeko told City’s website.
“I think Manchester United will drop points sooner or later but we just need to keep winning and keep the pressure on them.”
Dzeko also singled out David Silva for special praise after the midfielder netted both of City’s goals against the Cottagers at Eastlands.
“David took his goals really well and he is disappointed he didn’t maybe get a third, but I’m really pleased for him,” Dzeko added.
Manchester City travel to Queens Park Rangers in their next Premier League fixture on 29 January.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news