(Corrects 5th paragraph to show scoping study was completed)...

(Corrects 5th paragraph to show scoping study was completed)

SYDNEY, Feb 12 (Reuters) - The Australian government said it is weighing a proposal from a consortium including hearing implant maker Cochlear Ltd (COH) to buy a state-owned hearing service, a move likely to create headwinds from an electorate sensitive to privatised health.

In a statement on Friday, Finance Minister Mathias Cormann said the government was approached by a group which also includes the Royal Institute for Deaf and Blind Children and Sydney-based Macquarie University.

"The government will formally examine the proposal put forward by the consortium," the statement said, without giving a dollar value of the service. Australian Hearing's latest annual report says it grew pre-tax earnings by 77 percent to A$33.2 million in fiscal 2014/15.

A sale would be a tough sell for a conservative government already under pressure to prove it will leave Australia's subsidised public health system intact while it looks for ways to cut spending.

The government last year completed a scoping study into the possible sale of the hearing service, Australian Hearing, but postponed making a decision on whether to proceed, under pressure from opposition politicians and the health sector.

Federal and state governments are feverishly selling assets to cut debt and fund capital works amid a massive decline in tax receipts from the mining sector due to the commodities downturn.

The federal government in 2014 sold state-owned health insurer Medibank Private Ltd (MPL) in a sharemarket listing for A$5.8 billion.

It is also considering bids for the registries arm of the Australian Securities and Investments Commission, a sale expected to fetch about the same as Medibank.