The two teams clash on Sunday for the Manchester derby and the Scotland international thinks the game could help determine who will win the title.
Fletcher see City as a genuine threat for the first time this season having built a strong team over the summer.
"The Manchester derby has always been massive, but now City are genuine title contenders for the first time, that makes it even bigger," said Fletcher to the Daily Mirror.
"In previous years, it was bragging rights in the city if you won - it's a lot more than that now.
"For years, City weren't really a threat to us in the league. The derby was always a big game, but now it's huge in terms of the points at stake and where the title may end up at the end of the season."
However, the midfielder, who will almost certainly slot into defence thanks to a spate of injuries to team-mates, still believes that United stand alone with regards to their history of success.
He added: "We don't want to give City the confidence of winning trophies to get to our level. Our job is to keep Manchester United on top and as long as we keep on winning the big titles, it means they're not winning them.
"If City were to go on a run of winning a lot of trophies, then they would become a global club. But for world recognition, United stands out alone.
"The great thing about United is the history of the club. No-one can take away the Busby Babes, the Munich tragedy - all of these things are engrained in the club's history.
"United is known all around the world for its history and success, which is what makes it so strong and such a special club.
"Teams like Chelsea have won trophies and built on that success, but that's been maybe over a 10-year period.
"They still don't have the global appeal and size of Manchester United and that's how we want it to stay."