Scholes, writing in a blog for a bookmaker, feels Moyes has been made too much of a scapegoat for the poor 2013-14 season.
He suggested more questions needed to be asked of Woodward after Moyes's sacking and a series of frustrating transfer experiences in last summer's window.
"David Moyes took a lot of stick, but I believe he's a top manager
I'd question if 10 months was enough time," Scholes wrote in his new Paddy Power column published on Thursday.
"Edward Woodward has an awful lot to prove this time that he's good enough at his job
He has to bring the players in that the new manager wants.
"It's obvious that last year he didn't manage to do that
If he doesn't we are not going to get anywhere near the top."
Scholes, 39, retired a year ago but was brought back to United in a coaching role for the final four games of last season by interim manager Ryan Giggs.
He has not been told whether he will continue under new manager Louis van Gaal next season, but is not expecting to be retained.
Scholes said: "I've not spoken to Edward Woodward
I came back for Ryan Giggs for the last few games of last season to try to help out, but I'm not waiting for a phone call and don't expect to be at United next season."
Source : AFP
Source: AFP