Australian Security Intelligence Organisation director-general Mike Burgess said he would not be drawn into politicising national security issues after government ministers used his speech last week to suggest the opposition had been infiltrated by foreign powers.

It comes days after Defence Minister Peter Dutton alleged the Chinese Communist Party had "picked" Opposition Leader Anthony Albanese as their preferred prime minister during Question Time.

Nine newspapers reported a sophisticated spy ring had attempted to get Labor candidates in NSW elected in the upcoming federal election, according to unnamed security sources.

Mr Albanese and NSW Labor have since dismissed the claims as untrue.

The domestic spy boss publicly revealed last week in his annual threat assessment that a wealthy "puppeteer" with deep connections to a foreign government and its spy agency had planned to undermine an Australian election by compromising candidates.

The jurisdiction of the election, including whether it was upcoming or in the recent past, was not revealed.

Labor senator Kimberley Kitching used parliamentary privilege on Monday evening to name who she suspected was the "puppeteer".

Mr Burgess said he would not make any comments after the Victorian senator asked whether he could confirm wealthy Chinese businessman and philanthropist Chau Chak Wing was the spy ring's leader.

"I think it's unfair that you asked me that question in public," he said in response.

Mr Burgess refused to divulge any further details about the plot, including confirmation over whether it was related to a specific political party.

"ASIO is not here to be politicised and should not be," he said.

"We're here to protect Australians from threats [to] their security."

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Mr Albanese refuted the claims made against him by Mr Dutton on Friday morning as "nonsense", adding that no concerns had been raised with him by ASIO about any Labor candidates.

"I can't be clearer than that," Mr Albanese said.

While Mr Burgess said he did not want to comment on speculative media reports, he said the Labor leader had given an "accurate account".

He added the intelligence agency's work was in the national interest, "not sectional interests or partisan interests or personal interests".

"Where it is misused, that's a problem. But I can assure you where it is misused, if it was hypothetically misused, I would look at whether I needed to do an investigation for my own organisation," he said on Monday.

"Of course, we take this matter very seriously. We hold ourselves to the highest level of account."

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