The Red Devils have endured a tough start to the season under the former Everton coach, but the ex-England captain is confident that the Scot can turn things around.
"I'm a Manchester United fan, I have faith," Beckham told Sky Sports News. "We've got a very good manager, we've got a great setup as we did last year and we were champions last year.
"There's no reason why they won't be fighting for the title at the end of the season. Things can turn around, Manchester United is Manchester United at the end of the day. Sir Alex Ferguson has always said that when a player leaves, the club moves on.
"It will be the same, the manager's left but the club will move on because they're Manchester United and they have another great manager like David Moyes."
United sit in eighth spot in the Premier League, having already lost three times this season.