The England striker, 26, believes the Gunners – who the Red Devils will face at the Emirates Stadium on Sunday – have vastly improved over the course of this campaign.
Rooney credits manager Arsene Wenger for their rejuvenation and he believes results like the 8-2 thrashing at Old Trafford are a thing of the past for the London club.
“It wasn't just that one result. It was the way they started the season,” he told the club's official website.
“They didn't get the results they needed and a lot of stuff was said about them.
“But since then, they have gone on a great run and won a lot of games, as any team under Arsene Wenger is capable of doing.
“I certainly wouldn't write them off.
“They are capable of going on a big run and whilst I still think us, City and Tottenham are the three favourites, Chelsea and Arsenal could still have a big say in it.”
Tottenham are two points behind second-placed United while the reigning champions sit three points adrift of league leaders Manchester City.
Rooney, who has won four Premier League titles at Old Trafford, said: “Tottenham and City are both new to the challenge of the league.
“In previous years it has been Chelsea, Arsenal and Liverpool all the time.
“It is great for the league that so many teams can win the league now.”
Rooney dismissed any possibility of the game on Sunday coming down to the performances of him and Gunners striker Robin van Persie, and insisted whichever side wins will do so because of a team effort.
“It is not about me and Van Persie,” he said.
“It is about us against Arsenal. That is what we will be focusing on.
“There are a lot of top strikers in the league; Van Persie, Sergio Aguero, Yakubu is playing really well."
However, the former Everton forward accepted that the Netherlands attacker will be a major threat up front for the home side.
“Van Persie has scored a lot of goals and is playing really well,” the 26-year-old added.
“He will be the biggest threat for Arsenal on Sunday. Van Persie and Ramsey are certainly the two who have stood out for them this season.”