In a statement to the ASX, Healthscope described the bid as "unsolicited and conditional" noting that the bid was subject to due diligence, debt financing, foreign investment regulator approvals and each member of the consortium gaining internal approvals.

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"The Healthscope board has commenced an assessment of the proposal," the company said in a statement.

The indicative price of the offer would be reduced if dividends or other distributions were paid, it added.

Neither Healthscope, the consortium or AustralianSuper was prepared to comment on Thursday.

Healthscope has been under pressure as private insurers have sought to cut costs and have pushed hospitals to reduce charges and increasingly used public hospitals as a cheaper option.

At the same time, consumers are dropping out of the private health insurance market in the face of steepening premium rises.

Under the terms of the proposal, AustralianSuper has agreed it will not support any rival bid substantially lessening the chance of a rival bid.

Healthscope's share price surged 14.78 per cent on the news to close at $2.33 on Thursday. Healthscope was floated on the ASX out of private equity ownership in 2014 at a issue price of $2.10 per share. Its price peaked at $3.16 in 2016 but has been on the slide over industry pressures that have seen it issue two earnings downgrades.

Ben Gray, a principal at BGH, was heavily involved in the earlier previous private equity experience when he was local head of TPG.

In a note to clients, Citi analyst Victor Windeyer said the bid appeared to be opportunistic partly because the company's large project, the $840 million Northern Beaches Hospital, was about to open and would go from being a cost to being an earnings contributor in the next financial year.

He said a deal would more likely be struck in the range of $2.56 to $3.33 per share, the bottom end of the range representing the three-year average multiple of profit before interest, tax, depreciation and amortisation (EBITDA). The upper end would be hit if a 30 per cent control premium were applied.

Mr Windeyer said the offer was "highly conditional".

"It's a good price, it's a positive result for shareholders," said Danial Moradi, equity strategist at Lonsec Research.

"The company's been underperforming for 18 months now. For the share price to get to higher levels, they would have had to do something they haven't done in the past couple of years."

Healthscope owns 45 facilities around the country and has hired UBS to handle the approach.

Morningstar analyst Chris Kallos said the offer was in line with his valuation and that it was unlikely the deal, if successful, would result in the usual cost-cutting approach of private equity.

"There comes a point where you've stripped out all the cost that you can and you've actually got to spend money to enhance something," said Mr Kallos.

Another major shareholder in Healthscope is Ellerston Capital, with about 9 per cent. Ellerston did not respond to a request for comment.

With wires