Oldham parted company with former manager John Sheridan on September 25 following a poor start to the campaign.
The ex-England global, who has worked as a television pundit since retiring from his playing career in 2013, is a boyhood Oldham fan.
Sheridan left Oldham at the foot of the table but they have risen to 19th under the temporary management of Richie Wellens, their former midfielder, who wants the permanent job.
Former AC Milan gaffer Clarence Seedorf was thought to be a candidate for the vacant post, but is apparently no longer in contention for the job.
During a glittering playing career Scholes hoisted 11 Premier League titles, three FA Cups, two League Cups, along with a brace of Champions League triumphs.
Scholes turned down the chance to become Oldham manager in 2015 in the belief the timing was not right but chairman, Simon Corney, has claimed publicly in the past that he believes the 42-year-old will manage the club "one day".
Oldham are now under the stewardship of interim boss Richie Wellens, who has been credited with showing interest in taking charge of the club on a permanent basis.
Scholes has been linked with the Latics before, only for nothing to materialise, while he worked with the club's youth team in order to gain his UEFA A Licence.