"The obvious candidate is David Kidwell because he has been assistant coach over the last three years," Hayton said.
"He's in the system, knows the culture and we have had a discussion with David and we're also talking to a couple of other people.
"We'll work through that process over the next couple of days and hopefully we can make an appointment quickly so that we can move on."
Kearney contacted the NZRL last weekend to advise he was close to signing with the Warriors and would be standing down from his post as national coach.
Hayton admitted the timing of his departure was not ideal but said Kearney has offered to head to Perth to help ease the transition for the new coach in the lead-up to the test against the Kangaroos at Nib Stadium.
The 44-year-old however will not be going on to the UK as he turns his attention to his new role with the Warriors.
"Stephen has offered to go to Perth and transition and help do a transition if the new coach would like that support," he said.
"But he has also indicated he couldn't commit to going to the UK.
"Is the timing perfect, no, but these opportunities don't come up too often.
"It's a fantastic opportunity for him and we're really happy for him.
"We wish him and the Warriors all the success."
While Kidwell is the standout candidate to step into the role, Hayton confirmed the lack of top quality New Zealand-born coaches meant consideration would be given to appointing a foreign coach with the right credentials.
"There aren't many Kiwis within high profile positions within rugby league coaching ranks so we have to be open to someone else.
"And then it would really very much come down to their personality and their understanding of what we are trying to achieve as a team."