TV3 has also said it has a copy of the tape, but has not aired it.
Police say 'about four' other media organisations will be served with a search warrant.
TVNZ's political editor Guyon Espiner reported on the broadcaster's Midday programme that TVNZ had been told to expect a search warrant.
Herald on Sunday Editor Bryce Johns says he has had no approach from police this week.
Radio New Zealand's head of news, Don Rood, says the organisation is refusing to hand over any material gathered by news staff to police.
Police have told him that they will get a search warrant and execute it today or tomorrow.
The broadcaster's Checkpoint programme ran an interview with Bradley Ambrose, the cameraman who made the recording.
Brash - Key looks like he has something to hide
Meanwhile Act Party leader Don Brash this morning conceded the Prime Minister's decision not to allow the release of the so-called teapot tape made it appear as though he had something to hide.
Dr Brash told Radio New Zealand there was high public interest about what was on the tape, and by not allowing the release, it appeared Mr Key and Mr Banks had something to hide.
He was not concerned about the possibility Mr Key and Mr Banks were discussing the future of the Act Party leader.
"I'm not worried about that at all.
"I currently plan to stay as leader of the Act Party."
Dr Brash said "important policy" announcement were not getting media coverage because of the controversy.
"It's a serious distraction."
He said he might talk to the PM about the possibility of allowing the release of the tape so as to defuse the controversy, but the decision to release the tape was not for him to make.
"That's not my decision, essentially the Prime Minister was hosting that cup of tea and it is his decision."
Dr Brash said the Prime Minister's decision to refer the matter to the police made it had for him to backtrack on the tapes.
He remained confident the Act Party would be returned to Parliament, despite poor polling both in Epsom and nationwide.
"I think most people in Epsom know that the National Party won't get in by itself ... Act is the obvious ally to National."