National leader Simon Bridges has reportedly received an anonymous text from a person claiming to have leaked his expenses - and they say they're a National Party member.

Bridges and Parliament's Speaker Trevor Mallard both received an anonymous text message last week from a person claiming to be responsible for leaking the information to Newshub, sources told RNZ.

The text author reportedly said they had leaked the expenses because they disagreed with Bridges' leadership style, describing him as "arrogant", and wanted him to be held to account for his spending of taxpayers' money.

The author of the text warned they had suffered from mental health problems in the past and said being exposed publicly could push them over the edge and put their life at risk.

The appeal came after Mallard launched an inquiry into who leaked the expenses and promised to name and shame the person responsible.

Sources say the text was extensive, and was sent from a disposable phone.

National MPs are heading to Wellington for a meeting, and Bridges is likely to respond this morning.

Mallard told the Herald this morning he will be making no comment on anything to do with the incident or the inquiry until the terms of reference are prepared: "end of story".

Newstalk ZB political editor Barry Soper has told Mike Hosking Breakfast that he understands it isn't a National Party MP.

"It could be anyone with a burner phone," Soper said.

"To me it's a storm in a teacup.

"Some National MPs are on their way to Wellington today, but not for a spill. It's a show of support for Bridges for when he speaks to the media this morning.

"It was quite a detailed text but, as I understand it at this stage, it isn't a National MP – but we'll have to wait and see."

RNZ said it had not seen the text, which is believed to have detailed a number of conversations and pieces of information from National caucus meetings over a period of weeks in an attempt to prove the author was a National MP.

RNZ said Bridges declined to comment when contacted last night.

The Mike Hosking Breakfast has sought comment from Bridges.

Mallard has appointed former solicitor general Michael Heron to investigate the leak, which showed Bridges had spent $113,000 in a three-month period on travel expenses and Crown limo costs.

Announcing an inquiry, Mallard said he believed someone had deliberately undermined the system, and the security of MPs was important.

"Unless they have incredible expertise they will be identified," he said.

Mallard believed the inquiry was a good use of taxpayer' money.

"Members of Parliament will not be able to do their jobs properly."