The Greens say they can be swayed to back the privatisation of Australia's largest health insurer, Medibank Private, if the sale proceeds are directed to the public health system.
However, they remain cautious on providing full support for the move.
"It would be fair to say that if the sale was to go ahead, we would absolutely want to see that money invested into public healthcare," Greens' health spokesman Richard Di Natale said.
Senator Di Natale said Medibank's hearty dividends to the federal government strengthened the case to hold on to the business, which made a $126.6 million profit last financial year, down 57 per cent.
Since it converted to "for profit" status in 2009, Medibank has paid hundreds of millions of dollars in dividends to its owner, including "special" dividends.
Labor said recently it had no plans to privatise Medibank but Mark Fitzgibbon, head of listed health insurer nib, has long called for a sale.
In a move interpreted as boosting its corporate credentials, Medibank recently appointed former CSL director Elizabeth Alexander as its chairman.
Senator Di Natale also cast doubt on whether a Coalition government would reverse the means-testing of private health insurance, saying an Abbott-led government might be tempted to maintain the revenue once in power.
"They've made so many promises that they're not going to be able to keep that I suspect that some of the talk is probably very cheap," he said.
"So if they don't get around to it, it's not that they don't think it's a bad policy - it's because they're going to save pennies every way they can."
He said that although the Greens traditionally believed the sale of public assets "rarely produces a dividend for ordinary citizens", private health insurance was a special case.
"You really have to ask the question: should the government have a role in the private health insurance industry and would that money be better invested in the public healthcare sector?", he said.