Savage thinks that their "fear factor" has gone since the retirement of Sir Alex Ferguson, and tipped them to finish outside the Champions League qualification places.
"I don't think Manchester United are going to finish in the top four this season – because the fear factor among visiting teams has gone," Savage wrote in his column in The Mirror.
"Visiting opponents are not scared of United any more. In previous years, when you lined up in the tunnel before kickoff and glanced across at a cast of household names, you were beaten before a ball was kicked.
"As I've said in this column before, I like David Moyes and I believe he should be given time to build his own dynasty at United - Sir Alex Ferguson was always going to be an impossible act to follow. However, recent Premier League results at Old Trafford don't paint a false picture."
United travel to Fulham this afternoon.