The next governor-general could be announced before the end of the week.
"We're getting pretty close to reaching a conclusion," Prime Minister John Key told reporters today.
"You might find out sooner than you think - possibly this week."
And Mr Key doesn't think former politicians should hold the position.
"I don't think they should, as a general rule that's not my preference," he said.
That seems to rule out media favourites Dame Jenny Shipley and Jim Bolger, both former prime ministers, and Sir Don McKinnon, a former foreign minister.
Others who are being mentioned include Chief Justice Sian Elias and Dame Patsy Reddy, the lawyer who worked with Sir Michael Cullen on the review of the security agencies.
Governor-General Sir Jerry Mateparae, who had a distinguished military career, ends his five-year term on August 31.
Sir Jerry's predecessor was Sir Anand Satyanand, and he followed Dame Silvia Cartwright.
Sir Anand and Dame Silvia were judges, but Mr Key doesn't think a legal background is essential.
"In the end you need someone who can carry out the duties and responsibilities of the governor-general with the mana and respect that office deserves," he said.
"Sir Jerry didn't come from a legal background but he's done an outstanding job."
The governor-general is appointed on the recommendation of the prime minister.