Former Latics striker Bunn has been interviewed and was the favourite to succeed John Sheridan at one stage.
But now sources suggest ex-Leeds United chief Evans and McCall, a former Bradford City player and boss, are the frontrunners.
McCall, who is a Scotland coach but has been out of management since leaving Rangers last year, is also being linked with Bradford.
Evans last month became the sixth manager to be sacked by Leeds inside two years.
The Scot led Rotherham United to promotion to the Championship in 2014.
Oldham, who host Town in a pre-season friendly on Saturday, July 16, finished 17th in League I under Sheridan, appointed in January.
The Latics, who last week sold keeper Joel Coleman to Town for a reported £100,000, Athletic have only seven players signed up.
They are Connor Brown, Jake Cassidy, Rhys Murphy, Liam Kelly, Carl Winchester, George Edmundson and Danny Byrnes.