Woodcock, who also played in Germany, thinks that Schalke would be a great club for any manager.
With Moyes refusing to commit to a new deal at Goodison Park and the Royal Blues keen to speak to him, a move could be in the offing.
"It would be a great club for most managers," Woodcock told the Express.
"You get 70,000 every game in a fantastic stadium. You'd get 20,000 over there just watching the shirts dry.
"David Moyes has done a fantastic job at Everton. This might be a really good time to branch out."