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".
The former Manchester United midfielder, who retired in 2013, is reportedly in talks with the club following John Sheridan's sacking last month and met with Oldham officials earlier.
Oldham have also spoken to Clarence Seedorf about the manager's job, although the former Netherlands global is now out of the running.
Another ex-United player, Richie Wellens, is now caretaker manager.
Trump interview with Hannity in Harrisburg: How to watch
A White House spokeswoman did not immediately respond to CNBC's request for additional information about the president's comments. Twice a day, as the American flag is raised and lowered on USA military bases and other installations, a bugle plays "Retreat".