United have more silverware in their trophy cabinet, but City have had the better of their local rivals during the last couple of years.
Last November's 1-0 victory at the Etihad Stadium was the fourth successive derby win for City
The last time they achieved that feat was 60 years ago.
United have never lost five straight matches to their local rivals and Young wants to end City's dominance this weekend when the Blues come to Old Trafford.
"That's something you want to put right," the United winger said when asked about City's recent dominance in this fixture.
"It will be another massive game."
Despite City's recent success in derbies, United go into the match as favourites after registering five straight league wins.
That run has helped United move into third, one point ahead of City, who slipped to their third defeat in five games at Crystal Palace on Monday.
Young thinks United have a good chance of defeating the Barclays Premier League champions if they maintain their current form.
He said: "We know it will be tough but as long as we can play the way we have shown, especially in the last few games, and add to that, it's going to be a great game and hopefully we will get the three points.
"We want to keep the momentum going and the positive play."
Finishing above City would represent a major coup for manager Louis van Gaal, especially after the way his team started the season.
But, wary of the fact that seven matches remain, Young is not letting himself get too carried away despite United's recent upturn in form.
"It would be nice (to finish above City) but we are just taking each game as it comes," the 29-year-old said.
"It is obviously going to be another tough one against City next week but we will prepare as well as we can do as we always do."
Young's form has been key to United's recovery
The former Aston Villa midfielder has been so good recently that he has kept record signing Angel di Maria out of the United team.
That has not been enough to get him back into the England squad though.
Many tipped Young to earn an England recall after 19 months in the wilderness, but manager Roy Hodgson left him out of his squad to face Lithuania and Italy.
Young revealed Hodgson did not call him to explain his absence from the 24-man party when it was announced.
"There was no conversation (with Hodgson)," said Young, whose last England cap came against Ukraine in September 2013.
"Obviously I will always want to represent my country
I was a little bit disappointed not to be in the squad, but I have just got to make sure I am playing well here at United and hopefully I will get the call at some time soon."
Source : PA