Scholes was working as a pundit for Manchester United’s Champions League clash against Young Boys on Tuesday.
Jose Mourinho has made it clear he was not happy at the club’s transfer business in the summer.
The Portuguese gave Woodward a shortlist of targets at the beginning of the window.
However, when the market shut in early August, Mourinho was without a new central defender he craved.
Mourinho’s future at has been in doubt since and form on the pitch has not helped, with Manchester United down in seventh in the Premier League, already 14 points off top spot.
And Scholes claims the 55-year-old looks alone at the club after a falling out with Woodward.
“He seems like a lonely man at the minute doesn’t he,” Scholes said on BT Sport.
“He seems the man stuck in the middle of everything.
“He’s fallen out with the people who are trying to buy players for him, he’s having a pop at his players.
“He just seems a little bit alone in the middle of it all at the minute.
“And the way his team is playing it seems that way as well.”
Meanwhile, Liverpool legend Steve Nicol does not understand why Mourinho is still at United if his players are not following his instructions on the pitch.
“If the players aren’t listening to him, then what’s he doing there?” Nicol told ESPN FC.
“Just picking a team and then off you go?
“What do the board think when they hear a manager whose basically telling them that his players don’t listen to a word he says? Why is he there?
“If the players aren’t listening to you, what’s the point?”
And Luke Shaw admits United have lost their fear factor as teams feel they can go to Old Trafford and get a result.
Speaking on beIN Sports, Shaw said: “Off the back of the result on the weekend, I think it was always going to be tougher than we expected.
“Some teams used to fear Old Trafford but I think sometimes now people come in and think they can get results.
“Most importantly, that’s what we have got to change as a team and as a club — to bring that fear factor back to an Old Trafford that not many fear at the moment.”