England were unimpressive on Wednesday as they limped to a drab 1-0 friendly victory over Norway thanks to a second-half penalty from Rooney.
Roy Hodgson's men were heavily criticised following their group-stage exit at the World Cup and have since seen experienced midfielders Steven Gerrard and Frank Lampard step away from the international scene.
Scholes believes Gerrard's decision to retire from England duty has left the side bereft of any flair in the middle of the pitch and feels dropping former Manchester United team-mate Rooney deeper, behind a front three of Danny Welbeck, Daniel Sturridge and Raheem Sterling, could prove a useful solution.
Writing for his column in the Independent, ex-England and United star Scholes said: "It is quite obvious to me that we do not have a midfielder with the range of passing to exploit these three attacking players [Welbeck, Sturridge and Sterling].
"It is a radical solution, and one I would propose just for the Switzerland qualifier on Monday, but I would play Wayne Rooney in midfield. He is the best passer in the team and he can play that midfield role better than anyone.
"One thing you can be sure about Wayne is that he is not bothered about taking risks. If he saw the pass was on, he would hit it. If it did not work out, that would not deter him from trying it again and again. He would make that pass more often than not.
"The absence of a specialist midfielder capable of passing the ball with flair concerns me. Steven Gerrard could do it at his peak but he has stepped away from international football.
"Frank Lampard was never that kind of player. I look through the current squad and wonder who will provide the range of passing required.
"Moving Wayne would be a compromise for Roy Hodgson because this England team is not so blessed with goals that it can afford to lose its top goalscorer from the front line.
"During and after the World Cup I argued for Wayne to be played as a centre-forward but, with these three ahead of him, he could be a huge influence. And he could still make runs into the box."
