Kernan said that he had put his name forward for the job which became vacant when Brian McAlinden and Brian Canavan resigned at the weekend.
He emerged as the favourite for the post almost immediately due to his impressive track record with Crossmaglen Rangers, winning three All-Ireland club titles in the space of four years.
"I spoke to a county board member and told him that I would be interested. That's all I can say, my name is in the hat. I don't know who else is in for it," said Kernan.
"The reason I put my name down for it was, I suppose, solely down to not wanting to go to my grave without having a go.
"This job would be different because it means working with players I've hugely admired for their achievements over the last two or three years."
The Armagh county executive will discuss the managerial vacancy on Wednesday night, but are unlikely to rush into an appointment
Kernan has been out of the game since February when he relinquished his duties at Crossmaglen, but has recently been involved with Monaghan side Carrickmacross.
Canavan and McAlinden won consecutive Ulster titles with Armagh in 1999 and 2000 and whoever succeeds them has a tough act to follow.
Kernan is no stranger to the county scene having worked under Paddy Moriarty during his spell as manager.