Another former United midfielder, Richie Wellens, is now interim manager and has spoken of his desire to take on the role full time having won all three matches in charge.
The United great, 42, is an Oldham fan and rejected the chance to manage the club following Lee Johnson's 2015 departure.
At the start of this year, Scholes took youth training sessions at Oldham as part of work towards his Uefa A coaching licence.
Scholes has been an Oldham supporter since he was a child and he once expressed an interest in playing for them when he left Manchester United.More news: Former World Best Player, George Weah, Wins Liberia Presidential Election
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Scholes met officials from the League One side on Wednesday morning to discuss the possibility of replacing John Sheridan, who was sacked last month.
Scholes lives in the town and has been spotted at Boundary Park a number of times over the years.
The Latics lost seven of their opening nine games under Sheridan but have since turned their form around with three consecutive victories with caretaker boss Wellens.
Oldham are now 19th in League One and a takeover remains ongoing.
While Oldham declined to comment when contacted, it is understood Simon Corney, the owner, wants to make a permanent appointment as soon as possible.