The Scot has struggled in his debut season in charge at Old Trafford, and the champions are currently seventh in the Premier League, 18 points off leaders Chelsea.
Savage wrote in his column in The Mirror: "With heavy heart, but few alternatives, I've changed my mind about David Moyes.
"Moyes looks a pale, frightened man consumed by the pressure. I'm at the point now where I believe the job is too much for him. When my 10-year-old boy asks why Juan Mata is playing on the right and Marouane Fellaini on the left, and I have to tell him that I've no idea, something is badly wrong.
"United didn't spend £65m on those two players to use them in a formation so alien to their talents, so what is the point of giving their manager another £200m in the summer if there is no clear purpose behind the spree?"
United were beaten 3-0 by fierce local rivals Manchester City on Tuesday.