Last week Clarence Seedorf, the former AC Milan midfielder, ruled himself out of the running, after talks with the board. The club will decide whether to appoint him or Scholes in the next couple of days.
The ex-England global, who has worked as a television pundit since retiring from his playing career in 2013, is a boyhood Oldham fan.
Paul Scholes hosted training session for the club's youth team a year ago while working towards his UEFA coaching badges and has never hidden his love for the Latics.
They have moved up to 19th place, winning all three of their matches under interim manager Richie Wellens, but the Latics are actively pursuing a new boss.
Scholes originally hung up his boots in 2011, before returning to action six months later for a further season-and-a-half, ending in Premier league success under Sir Alex Ferguson, who then drew the curtains on his managerial career.
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.
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