Penrith coach Ivan Cleary said after the World Cup, at which he worked with Kearney, he was interested in remaining involved with the Kiwis, but he is unlikely to have the time or inclination to seek the top job.
Applications close on January 31. A six-man selection panel will then conduct interviews and recommend a candidate to the NZRL board by mid-February, with a view to an appointment being announced at the end of the month.
The coach's first assignment will be the Anzac test against Australia.
Kearney is known to have considerable support within the NZRL. There is a feeling that because of his experience and rapport with the players, it would be a mistake to make a change for the sake of it, and parallels have been made with the Rugby Union decision to reappoint Graham Henry as All Blacks coach despite the failed 2007 World Cup campaign.
Kiwis selector Richie Barnett thinks Kearney should be reappointed.
"I think Steve is the right person for the job and it's echoed by the players," he said. "The current management setup is the perfect model.
"I don't think they should mix with things, irrespective of what happened in the World Cup final."
NZRL high performance manager Tony Iro, who acted as Kiwis manager during the World Cup, has effectively ruled himself out by being a member of the selection panel.
NZRL chief executive Phil Holden, who is also on the panel, said he welcomed Kearney's decision to reapply.
"He's a strong candidate and someone we will be seriously looking at because he's the incumbent. He's been to two World Cup finals and won one and lost one. I was delighted he said he was going to reapply."