Last season City recovered from an eight-point deficit with six matches to go to claim their first Premier League crown, and Vieira believes that they can catch United again this campaign.
"There's still a long way to go. We still believe we have a good chance to catch them," Vieira told talkSPORT. "It will be more difficult than last season, of course, but we have to give it a go.
"When you look at Chelsea, ourselves and Manchester United, I think all three teams have a chance. Man United are in a really good position but what is interesting in this Premier League is anybody can drop points and the door is still open for us.
"We just have to look at ourselves. We know what we have to do and we will keep fighting."
City host Fulham in their next match on Saturday.