The Defence Department has referred the leaking of sensitive and classified information to the Australian Federal Police for investigation.

News Corp published correspondence between senior public servants at the Home Affairs and Defence Departments, which the ABC confirmed was about possible changes to the Government's cyber spy agency to monitor Australian citizens.

Defence Secretary Greg Moriarty discussed the unauthorised release with AFP Commissioner Andrew Colvin on Sunday, the Department said in a statement.

The Australian Signals Directorate (ASD) collects and assesses foreign intelligence information before passing it on to Australia's domestic and foreign spy agencies.

The ASD does not collect information on Australian citizens, but some senior public servants want to change that.

If the Government approved the proposal, which was first reported by News Corp, the agency could be given permission to access the emails, bank records and text messages of Australians.

The ABC understands the proposal has not been discussed at a ministerial level and Defence Minister Marise Payne — who is responsible for the agency — says no formal proposal has been submitted.

Foreign Minister Julie Bishop indicated she would not support the proposal if it came forward.

"There is no plan for the Government to extend the powers of the Australian Signals Directorate so that it could collect intelligence against Australians, or covertly access private data," Ms Bishop said.

"There is no such plan.

"I don't see any national security gap, and I certainly believe the current laws safeguard the privacy of Australians but also keep Australians safe."

The secretaries of Defence, Home Affairs and the ASD have issued a joint statement saying there is no formal proposal to restructure the agency.

"In the ever-changing world of cyber security as officials we should explore all options to protect Australians and the Australian economy," the statement said.

"We would never provide advice to government suggesting that ASD be allowed to have unchecked data collection on Australians — this can only ever occur within the law, and under very limited and controlled circumstances."

But the Opposition's Defence spokesman, Richard Marles, told Insiders it was clear the push was being discussed by some of Australia's most senior public servants.

"We need to be clear here — our nation's security and an accumulation of Peter Dutton's power are two different things," he said.

"It concerns me at times the Government confuses them.

"This needs to be seen as an asset of Defence and that's where it remains."

Mr Dutton is the head of the Home Affairs department, which is responsible for immigration, law enforcement, and national security.

His office referred questions to Senator Payne, who said "there has been no request to the Minister for Defence to allow ASD to counter or disrupt cyber-enabled criminals onshore".

Mr Marles and Deputy Opposition Leader Tanya Plibersek said they were concerned the information had been leaked to the media.

"That a proposed ministerial submission of this kind, has found its way onto the front page of the media today I think is enormously concerning," Mr Marles said.

Ms Plibersek said the information was highly classified and marked "for Australian eyes only".

"If you look at the documentation, it's 'For Australian Eyes Only', it's highly classified," she said.

"Who is it in government that is leaking highly classified information — perhaps to try and stop Peter Dutton's latest power grab?

"So the first question; is who's leaking, why are they leaking highly-classified documentation, and what is wrong with national security debates within the Government around the Cabinet table that people think they resort to leaking to get their own way?"

Labor's national security spokesperson Mark Dreyfus has asked the Prime Minister to investigate the leak and said it risks, "damaging the integrity" of the work security agencies do.

"I am deeply concerned that this national security leak is potentially a result of political tensions and divisions inside your government over portfolio responsibilities," he said in a letter to Malcolm Turnbull.