But the 53-year-old is playing the waiting game as the League I club consider all options, including former Norwich City boss and Latics player Neil Adams.
Bunn, also a former Oldham player, has been the bookies’ favourite to replace John Sheridan.
But sources suggest it’s far from cut and dried.
The Latics, who host Town in a pre-season friendly on Saturday, July 16, have lost Sheridan to League II Notts County.
They are now seeking a sixth boss in 15 months.
Bunn has had four successful years at Town and has just led his charges to Professional Development League II play-off success.
The former Wigan Athletic, Manchester City, Coventry City and Rochdale coach initially took charge of the Under 18s, who he led to two PDL II play-off finals and the last eight of the FA Youth Cup.
He has also taken the 21s to two play-off finals as well as the semi-finals of the Under 21 Premier League Cup.
Oldham, who this week sold keeper Joel Coleman to Town for a reported £100,000, have agreed a new deal with Northern Ireland midfielder Carl Winchester.