Australia's largest health insurer Medibank Private is looking to cut its apron strings with the federal government as it garners support for privatisation.
But Finance Minister Penny Wong has no plans to sell off the government's most profitable business - just yet.
Medibank, which insures 3.7 million Australians, now brings in more than $5 billion revenue per annum, slightly more than Australia Post.
Managing director George Savvides stressed that government ownership had not constrained the business as it expanded into health services over the past four years.
"But in trying to open up these new businesses we are absolutely asking these questions and our owners are too," Mr Savvides told a business lunch in Sydney on Thursday.
Taxpayers were examining Medibank's mandate and questioning why the government owned the business, he said.
However, Medibank could continue to provide efficient and effective public health delivery, Mr Savvides said.
"Do we need to be owned by the government to do that? Well probably not," he said.
"There's a time for every child to leave home. I'll leave you to finish that story."
Medibank Private would tread a well-worn path into privatisation, with the Commonwealth Bank, Telstra and Qantas leading a long line of public entities moving away from government ownership.
It would leave Australia Post as one of the last bastions of federal government ownership of a massive enterprise.
Last year, Medibank Private recorded its strongest financial performance in its 35-year history as it expanded through recent acquisitions.
The opposition has pledged to float the business if elected while critics worry about a lack of competition for consumers if it stays in public hands.
But Senator Wong's spokeswoman on Thursday said the government had no plans to sell Medibank Private "as per the commitment we made in 2007".
Mr Savvides also took aim at steep fees some doctors charged and called for tighter regulations.
Industry surveys showed customers who dropped out of private health insurance were often annoyed by their "gap experience," or the difference in the amount they paid compared to the amount for which they were covered, he said.
"There are quite a lot of doctors that can charge beyond (the basic fee) and they are allowed to and if the customer is not informed, it creates a very unhappy outcome," he said.
"The regulations are unfortunately not as robust and tight as we would like."