The ex-England star, who is a life-long Oldham supporter, has no managerial experience in the EFL but has coached at United since retiring.
The League One club declined to comment on reports linking Scholes with the vacancy created when John Sheridan was sacked last month.
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The 42-year-old, who has worked as a television pundit since retiring from his playing career in 2013, has met the Athletic hierarchy to discuss the manager's role.
Richie Wellens is the caretaker boss and is also a candidate for the full-time role.
Oldham are 19th in League One and next play Blackburn on Saturday.
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