Both were interviewed last week, BBC Radio Nottingham understands.
But Penney, who knows Stags chairman John Radford from their time together at Doncaster, has emerged as the likely replacement for David Holdsworth.
Holdsworth parted company with Mansfield in November
after less than two years in charge at Field Mill.
Former Darlington boss Penney left Oldham by mutual consent in May after just over a year in charge of the Latics.
Source: BBC Sport
Source: BBC Sport