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Scholes was employed as a coach under Ryan Giggs during the Welshman's four games in charge of United towards the end of last season.
The former United midfielder is yet to be given a role by Giggs' successor Louis van Gaal though.
Some believed Scholes' comments in an online blog for Paddy Power during the summer had reduced his chances of a return to the coaching staff at Old Trafford.
Speaking about his former teammate Rooney, Scholes wrote: "There's a chance he's worn out. Wayne's peak may have been a lot younger than what we'd expect of footballers traditionally.
"Age 28 or 29 has been the normal 'peak'. With Wayne, it could have been when he scored 27 league goals in 2011-12 when he was 26."
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The former England midfielder also hit out at executive vice-chairman Woodward for failing to land United's top targets last summer.
Scholes wrote: "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."
But despite the barbs, Press Association Sport reports the United hierarchy are keen for Scholes to have some sort of coaching role at Old Trafford next season.
One of the roles under consideration for the 39-year-old, who played 718 times for United, is as an assistant to Nicky Butt, who is in charge of the under-21s.