Both sides won difficult fixtures at the weekend with United beating Liverpool 2-1 and reigning champions City easing past Arsenal 2-0 at the Emirates Stadium.
Those results mean Sir Alex Ferguson's side still hold a seven-point lead at the top of the table but Zabaleta reckons a decent run of form could see City close up and overtake United, like they did in dramatic fashion last season.
"We know that we are up against a rival in United who are in a very good moment," he said.
"They have seven points more, but that is not much in this league. There is still a long way before the title is decided and there is still a margin to lose and recover.
"We hope United have a few games where they lose some points and we continue on this route, taking three points all the time."
Zabaleta's team-mate David Silva also knows what has to be done and admits losing just one game between now and the end of the season could cost the champions their title.
When asked if there was a sense that City could not lose again this year he said: "Yes, because if we lose, then suddenly the gap is 10 points, and that is when it gets really difficult. "But if we keep fighting, we hope that they will falter."