The ex-England midfielder, 44, co-owns National League club Salford City along with five of his former Manchester United team-mate and EFL rules prevent a person holding roles with two clubs at the same time without the prior consent of the board.
If appointed by Oldham, Scholes will take his first managerial role in the EFL with the club he followed as a boy.
His only professional involvement since he retired in 2013 has been the four games he spent as part of Ryan Giggs' backroom team when the now Wales manager took caretaker charge at Manchester United following David Moyes' dismissal as boss in 2014.
He has most recently been working as a television pundit for BT Sport.
Oldham, 15th in League Two, play Crawley away on Saturday.