Harrison told Sky Sports News: "I'm 100% for David Moyes, I really am, things are going bad for him and all that. The look on his face when he's on TV I feel so sorry for him.
"Sir Alex Ferguson will be having a word with him there's no question about that, but he won't be saying you've got to do this and that. He will do it nice and quietly.
"I think the pair should get together quite a lot and he should listen seriously to Sir Alex."
When asked if he saw Moyes turning things around at Old Trafford, he added: "At this moment in time, no."
Harrison also believes that Moyes made a big mistake in clearing out Ferguson's backroom staff and replacing them with members of his own staff from his time at Everton.
"In hindsight it does look like a mistake, I don't want to criticise anyone but I've got to be honest because if I'm thinking that why shouldn't I say it, like most of the Man United supporters," he added.
"They certainly should have kept the staff that they had, they shouldn't have brought so many in from Everton."