National claims that two or three MPs are yet to sign privacy waivers to allow investigators to look at their work computers and cellphones in search of a potential leaker.

But it is expecting all MPs to have signed the waiver tomorrow morning when MPs arrive at Parliament for caucus.

National leader Simon Bridges has delegated deputy leader Paula Bennett and shadow leader of the House Gerry Brownlee to oversee the investigation.

"There are a number - it's only like two or three maybe - that haven't signed because they are overseas," said Brownlee. "But they've said they are quite happy to sign and they'll be back in time for caucus tomorrow.

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"By the time of the caucus run tomorrow, they will all have been sorted," said Brownlee.

Asked who the MPs were, he said it was an internal investigation now, not a public investigation.

"So I'm not giving out any more information [other] than everyone has agreed to the proposal."

Tuesday's caucus is the first time the caucus has met since Speaker Trevor Mallard overturned his decision to hold an inquiry into who might have leaked National's travel expenses to Newshub.

On August 23 Mallard named Michael Heron, QC, to conduct the investigation followed a leak on August 13.

But he cancelled it on August 24 after it was publicly revealed that Newshub, Mallard and Bridges had received an anonymous text from someone claiming to be a National MP and pleading for the inquiry to be called off for the sake of his or her mental health.

Bridges was not entirely convinced it was from a National MP but Mallard said the text was from someone who was clearly very disturbed and publicity around the text would make that worse whether the person was an MP or a staffer.

The police know who the leaker is but are refusing to say. Bridges referred to the text to the police and they traced the person out of concern for their welfare.

Brownlee is not giving any guarantee that the result of the inquiry will be made public and hinted that if the culprit is identified and has genuine mental health issues that it might not be.

"That will entirely depend on the circumstances," said Brownlee.

It had been called off because of the Speaker's concerns about the mental health of an individual and there were many things to consider.

"We are not making any commitments one way or the other."

The investigation will look at traffic from National MP and staffers' computers. Mallard has also made computers of relevant Parliamentary Service staff who handled the documents available to the inquiry.

The inquiry is being conducted by PwC which will be assisted on issues of privacy by Simpson Grierson law firm on privacy issues.

It is understood that PwC is the same company that was going to work with Heron on the Speaker's inquiry before he cancelled it.