United have endured a turbulent start to Moyes' tenure as manager and currently sit eighth in the Premier League having already lost three times.
However, Beckham, who won the treble of Champions League, Premier League and FA Cup during a glittering playing career at Old Trafford, believes there is still plenty of time for Moyes' side to fight their way back to the top of the table.
"I'm a Manchester United fan, I have faith," he told Sky Sports News.
"We've got a very good manager, we've got a great set-up 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."