The 42-year-old is a life-long Oldham supporter, but has never held a full-time coaching job.
The northwest club declined to comment on the reports they had spoken to the former England midfielder about the job.
Scholes has been working as a television pundit and co-owns non-league club Salford City with some of his former United team-mates.
He won 11 Premier League titles, three FA Cups and two Champions League crowns during a 20-year playing career at Old Trafford before retiring in 2013.
Former Oldham player Richie Wellens has been in interim charge since John Sheridan left last month and the club are 19th in League One, a point above the relegation zone.
Ex-Netherlands midfielder Clarence Seedorf also held surprise talks with Oldham, but is now out of the running.