The ex-England midfielder owns a 10% stake in National League club Salford City along with five former Manchester United team-mates.
EFL rules prevent a person holding roles with two clubs at the same time without the prior consent of the board.
However, a holding of 10% or less in a club is disregarded providing it is held “purely for investment purposes”.
If appointed by Oldham, the 44-year-old will take his first managerial role in the EFL with the club he followed as a boy.
It is understood Scholes has previously spoken to the Latics about succeeding Frankie Bunn as manager, but the matter was complicated by his involvement with Salford, who could be in the same league as Oldham next season.
This issue has now been resolved, leaving Scholes free to take up the job at Boundary Park if it is offered.
Scholes, who co-owns Salford alongside Gary and Phil Neville, Ryan Giggs, Nicky Butt, David Beckham and businessman Peter Lim, has previously spoken of his desire to take up a full-time coaching or management role.
His only professional involvement since he retired in 2013 has been the four games he spent as part of 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, followed by successive home fixtures against Yeovil (12 February), Crewe (16 February) and Morecambe (19 February).
Academy boss Pete Wild has been in caretaker charge at the Latics since Bunn’s sacking on 27 December.