The Gunners currently top the Premier League having lost just one of their 10 matches this season, but Rooney has insisted that it is still early days.
"We'll have to wait and see where they are in March. We've seen before that they've been in the top two until February and March and then they've faded off, so it's down to them to try to stay there," he told reporters at a press conference.
"They're doing brilliantly at the minute and they're in a great position so it's up to us to catch them. We know we're capable of playing better and we're starting to do that; we need to start picking points up and see where we are come Christmas.
"We're nine or 10 games in so there's no big worry at the minute. We're starting to do well so, if we can get the victory on Sunday, I think we'll be in a great position."
Arsenal travel to United on Sunday.