Oldham, who parted company with boss John Sheridan on September 25, declined to make an official comment on the matter, but Goal and Omnisport understand Scholes held talks on Wednesday.
Ex-Netherlands star Clarence Seedorf was interviewed last month, but is now out of the running.
The Lactics have won three consecutive games in all competitions under caretaker manager Richie Wellens, who like Scholes is a product of the Old Trafford youth system.
Scholes, an 11-time Premier League champion, was previously offered the chance to become manager at his boyhood club when Lee Johnson left for Barnsley in 2015.
In a column for the Independent newspaper at the time, Scholes wrote: "One day I believe that I will manage Oldham, the club that my dad supports and who are very close to my heart.
"They are a really good family club who mean a great deal to a lot of people - myself included. I just did not feel this was the right time."
At the start of this year, Scholes took youth training sessions at Oldham as part of work towards his UEFA A coaching licence.
Since calling time on a United career comprising 717 appearances and 155 goals, Scholes has worked as a television pundit and briefly coached at Old Trafford in the aftermath of David Moyes' ill-fated reign.
Along old United colleagues Ryan Giggs, Gary Neville, Phil Neville and Nicky Butt, Scholes owns a stake in non-league side Salford City.