Oldham are searching for a new boss following the departure of Paul Dickov from Boundary Park last month.
Tony Philliskirk has been in caretaker charge of the side, but he ruled himself out of the running for the role on a permanent basis.
A host of names, including Paul Scholes and Iain Dowie, had been linked with the role, but Johnson has now come onto the radar for the job, according to Sky Sports.
Johnson, who is the son of Yeovil boss Gary Johnson, is currently without a club after leaving Kilmarnock in January.
The 31-year-old, who has no managerial experience, is understood to have been interviewed for the Oldham job and is said to have impressed the Latics board during talks.
Oldham could now offer Johnson the position as they look to climb clear of trouble at the wrong end of League One and secure survival.