David Moyes's side go into the match against the league leaders having won just two of their five home encounters this term, while they have also failed to defeat rivals Chelsea, Liverpool and Manchester City.
However, Higginbotham believes that there have been signs in recent weeks that the United squad have started to adapt to life under their new manager and as a result, he can see them getting the better of the Gunners, who will travel to Old Trafford on the back of a 1-0 win over Borussia Dortmund in the Champions League.
"A lot of people, probably even some United fans, will make Arsenal the favourites, even though it is at Old Trafford. That's interesting because normally United, whoever they play against in the Premier League, are favourites," the 34-year-old told Sports Mole. "Arsenal are where they are at the moment and they are playing some very good football. They had a great result during the week and it's going to be a difficult game for United.
"The thing is with United, they have big players for big occasions - they've been there and done it. I see no reason why they can't beat Arsenal. It will be a very tough game because Arsenal are the form team in the Premier League, but if United can beat them, it will set down a real marker.
"There has been signs over the last few weeks that things are starting to fall into place for United. It's a new era for everybody and there was always going to be some adjustments. There's been a few doubts about the team spirit, but they've rubbished that by coming back against Sunderland and Stoke when they were a goal down. I think they'll beat Arsenal and then kick on from there."
Arsenal have not won at Old Trafford since 2006 when Emmanuel Adebayor scored the only goal of the game.