The Government has flagged tougher rules on media ownership after a share raid reportedly gave mining magnate Gina Rinehart a 12.8 per cent stake in the Fairfax media empire.

Fairfax says Ms Rinehart doubled her stake in the company last night after buying up shares following the close of trade on the Australian Stock Exchange.

It is believed Ms Rinehart is seeking to increase her hold further to just under 15 per cent, which would make her the company's biggest individual shareholder.

Shares in Fairfax jumped more than 10 per cent to a three-month high at 81.5 cents.

The West Australian-based mining magnate is already Australia's richest person and already has a 10 per cent stake in Channel Ten, along with a seat on that company's board.

Who is Gina Rinehart? Daughter of mining magnate Lang Hancock

Daughter of mining magnate Lang Hancock Australia's richest person

Australia's richest person Personal wealth estimated above $10.3 billion

Personal wealth estimated above $10.3 billion Wealth has soared due to iron ore mining boom

Wealth has soared due to iron ore mining boom Championed opposition to Labor's mining tax and carbon tax

Championed opposition to Labor's mining tax and carbon tax Bought stakes in Channel Ten and Fairfax

Bought stakes in Channel Ten and Fairfax Read more

Now media analysts say the Fairfax move is almost certainly designed to increase her political influence, and say they expect her to push for a seat on the Fairfax board.

Communications Minister Stephen Conroy said Ms Rinehart was not breaking the law as it stands, but said he wanted new laws to include a public interest test on media diversity.

"Clearly she is seeking to exert her influence but is she breaking the law by exerting an influence? No," Senator Conroy told ABC Local Radio.

"Do we need stronger laws in this area? Yes.

"We want to see a debate around a public interest test."

The minister highlighted Ms Rinehart's well-known views opposing the Government's Minerals Resource Rent Tax (MRRT) on iron ore and coal projects.

"Mrs Rinehart's views on the mining tax are clear," he said.

"She doesn't believe all Australians should have a fairer share of the wealth that's being generated by the resources of this country, that are owned by every Australian. She doesn't agree with that.

"But governments cannot pass laws on the basis of who they like and dislike and whose views they like and dislike."

Sorry, this video has expired The Power Index's Paul Barry discusses Gina Rinehart's move to boost her stake in Fairfax media

This morning The Power Index's Paul Barry said he believed Ms Rinehart was out to influence the debate around mining and other issues.

"Well I don't think it's the money ... I think she wants influence and she wants a say in the debate," he told ABC News Breakfast.

"People around her have said she wants the miners to have a voice.

"She's already bought into Ten and she's succeeded in having some changes there and I think (buying into) Fairfax is the same process, which is her trying to get a voice in the media.

"I think she's definitely after that.

"That's one thing, whether she'll get it is another. It's going to give her a seat on the board but that's not going to let her dictate the policy of the paper."

Shadow treasurer Joe Hockey dismissed concerns that Ms Rinehart could be able to exert undue influence on the national debate.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Listen Duration: 3 minutes 3 m Mining magnate increases stake in Fairfax Download 1.4 MB

"It comes down to the quality of the paper, the quality of the editorial," Mr Hockey told ABC Radio National this morning.

"I think it arguably does not matter who owns the media company.

"The bottom line here is it has a strong board, editorial independence, and quite frankly Gina Rinehart is a good person and a good Australian."

The journalists' union says it would be concerned if Ms Rinehart was making the move to try to sway the nation's political debate.

But the Media, Entertainment and Arts Alliance's secretary, Chris Warren, said Fairfax papers would not be pressured if Ms Rinehart tried to exert influence.

"The fundamental strength of papers like the Sydney Morning Herald and The Age and the Financial Review and the many other Fairfax papers is their quite strong independence," he said.

"I'd remain confident that regardless of who the owners are, or who the shareholders are, the journalists of the paper will be very concerned to continue to defend the independence of those papers."

The Government has already been examining media regulations through the Convergence Review, which was set up in December 2010.

Senator Conroy says he supports its preliminary recommendation to introduce a public interest test. Its final report will be given to the Government in March.