Australian police are investigating a former senator's allegations that an executive from Rupert Murdoch's News Limited offered him favourable newspaper coverage and a "special relationship" in return for voting against government legislation.

Former Senator Bill O'Chee recently submitted the claims in a nine-page statement to police which were published on Wednesday by Fairfax Media newspapers, the major competitors of News Corp in Australia.

According to an article in the Guardian, the Fairfax Media newspapers reported that an unnamed executive of News Corp's Australian subsidiary, News Limited, asked O'Chee, during a lunch on June 13, 1998, to vote against his government's legislation on the creation of digital TV in Australia. News Limited stood to profit from the legislation failing.

In a statement on Wednesday, Australian police said O'Chee's allegations have been under investigation since Nov. 4.

"As this matter is ongoing it would not be appropriate to comment any further," the statement said.

Offering a senator a bribe or incentive to influence a vote is an offence punishable by up to six months in prison.

The claims are humiliating for News Corp, whose ownership of 70 per cent of Australia's newspapers has raised objections that Murdoch's empire has too much control over the country's media.

The government has opened an inquiry into strengthening newspaper regulation in Australia, following the close of News International's leading British tabloid, the News of the World, in July over illegal phone hacking.

As the former senator for the state of Queensland, O'Chee was renowned for voting against his National party's desires. He claims the News Corp executive told him that while voting against the digital TV legislation would attract criticism, "we will take care of you".

The executive "also told me we would have a 'special relationship', where I would have editorial support from News Corp's newspapers, not only with respect to the ... legislation but for 'any other issues' too," O'Chee reportedly told police in his statement.

"I believed that [he] was clearly implying that News Corp would run news stories or editorial content concerning any issue I wanted if I was to cross the floor and oppose the ...legislation."

In the week following the lunch meeting, O'Chee said he contacted the executive to inform them that he had decided to vote for the legislation.

"After this conversation it became almost impossible for me to get anything published in the Queensland newspapers which News Corp controlled, even though I had been able to do so before the lunch meeting," O'Chee reportedly said in his statement.

Four months after the lunch, O'Chee lost his senate seat at elections.