Greens senator Scott Ludlam says he will write to Communications Minister Stephen Conroy and his opposition counterpart Malcolm Turnbull on Tuesday asking them to support legislation that would ensure media owners and board members could not obstruct objective and independent journalism.
The Greens' solution could include regulations or an amendment to current broadcasting laws.
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"We're not looking to a knee-jerk solution here," Senator Ludlam said.
"We're looking to something that would have integrity and that would actually serve working journalists and the general public."
The Greens said they would consider introducing legislation before the end of next week, when parliament breaks for six weeks.
Greens deputy leader Adam Bandt said a strong, healthy democracy relied on well-resourced and independent journalism.
"It's clear that she's wanting to control what to date has been a very important and independent newspaper and house of journalism for the purposes of influencing public debate," he said.
The plan to introduce the new laws comes after mining magnate Ms Rinehart increased her stake in Fairfax Media to 18.67 per cent.
She has been seeking a position on the board of Fairfax since becoming its major shareholder at the beginning of 2012.
The news of her increased stake came as Fairfax announced major changes to its newspaper business, which will result in 1900 staff cuts in the next three years.
Mr Bandt said the people affected deserved as much support from the federal government as manufacturing or any other worker in the country.
"That's 1900 jobs and 1900 families that deserve our support," he said.
