Woodward came in for criticism for the way United conducted their transfer business before the 2013-14 season, with a number of targets reportedly falling by the wayside.
And Scholes, who returned to assist Ryan Giggs in his four matches in charge at the end of the season following the departure of David Moyes, says Woodward has to show his credentials in such an important role in the upcoming months.
"Edward Woodward has an awful lot to prove this time that he's good enough at his job," Scholes wrote in a blog for Paddy Power.
"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 also said that the first player he would bring in would be Bayern Munich's Toni Kroos and, despite helping Giggs out at the end of the season, does not expect to be asked to follow the Welshman in joining Louis van Gaal's backroom staff.
"I came back for Ryan Giggs for the last few games to try to help out but I'm not waiting for a phone call and don't expect to be at Old Trafford next season," he added.
"Louis van Gaal has the credentials. He's been at the biggest clubs in the world but he has a major job on his hands at Man United.
"It's a massive task and there’s a big gap to fill to catch Man City, Chelsea and Liverpool next season. United are a long way behind. If Van Gaal gets them to the Champions League, it'll be a start."
