Richard Alston has said that he can still win support for the new bill, despite the fact that the main opposition, the Australian Labor Party, remains opposed to the changes.
Alston is reported to have said: "I've had discussions with certain people and I think the game is still alive, certainly. I think it's just then a matter of perhaps assuaging some lesser concerns and hopefully getting majority support."
If the law is changed, it is almost certain to see a bidding war start for Fairfax Holdings, the company behind newspapers such as the Sydney Morning Herald and The Age.
Irish media magnate Sir Anthony O'Reilly is known to be interested in acquiring Fairfax as part of his Independent News & Media group, and other publishers including Dow Jones are also believed to be interested.
Australian media-ownership laws currently prevent foreigners from owning more than 25% of a mass-circulation newspaper.
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