Former All Blacks assistant coach and current Crusaders boss Robbie Deans, the bookmakers' favourite, has an opportunity to return to international rugby after a three-year hiatus.
Hurricanes coach Colin Cooper and Chiefs' Ian Foster, who have jointly led the Junior All Blacks to back-to-back Pacific Nations Cup wins without losing a game, were also interviewed.
Deans told media assembled outside the union offices: "It's heart and head. I've got a passion for it and I believe I've got something to offer in terms of what I bring to it as well.
"It doesn't matter what I think though, does it? It's what they think that's the priority.
"These guys have got a responsibility and they take that responsibility seriously. They'll make their decision. It will be in the best interests of New Zealand rugby."
Cooper, a former assistant to Deans at the Crusaders, was the first to be interviewed. On leaving, he said: "Having an opportunity to talk about what you could bring was great.
"We tell our players to aspire to become All Blacks and it has always been a goal of mine to be part of the All Blacks."
Foster said: "When you get down to the final four for the All Black job you want to become the All Black coach.
"There have obviously been two leading candidates for this process so I wanted to make it clear that I was confident I could do the job. I had a chance to express myself, which is all you can ask for."
Should Henry, who did not speak to the media, retain the role, he is likely to retain current assistants Steve Hansen and Wayne Smith.