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.

Bill O'Chee made the allegations in a nine-page statement to police and they were published on Wednesday by Fairfax Media newspapers, rivals of News Corp's Australian subsidiary.

The newspapers reported that an unnamed executive of News Ltd asked O'Chee during a lunch on 13 June 1998 to vote against his conservative government's legislation on the creation of digital TV in Australia. The news group stood to profit from the legislation failing.

The Australian federal police said in a statement on Wednesday that O'Chee's allegations had been under investigation since 4 November. "As this matter is ongoing it would not be appropriate to comment any further," the statement said.

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

O'Chee did not return an Associated Press phone call on Wednesday and a News Ltd spokesman did not immediately respond to a request for comment.

The allegations are embarrassing for News Corp, whose ownership of 70% of Australia's newspapers has raised criticisms from within the government that Rupert Murdoch's empire has too much control over the country's media.

The government has opened an inquiry into potentially increasing newspaper regulation in Australia after News International closed its top-selling British tabloid, the News of the World, in July over illegal phone hacking.

O'Chee, a former senator for the state of Queensland with a track record of voting against his National party's wishes, alleged the executive told him that while voting against the digital TV legislation would be criticised, "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."

O'Chee said that a week after the lunch he called the executive to say 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.

He lost his senate seat at elections four months after the lunch.

O'Chee had been discussing that inquiry with an unnamed Australian lawmaker at an Australian airport recently when he mentioned his allegations against the executive, Fairfax media reported. The allegations were then referred to police.