SYDNEY, June 30 (Reuters) - Buyout firms TPG Capital and Carlyle Group are aiming to raise as much as A$2.57 billion ($2.42 billion) in an initial public offering of shares in Australia's Healthscope Ltd, making it the country's third-largest ever listing.

In a prospectus lodged on Monday, Healthscope said it would raise total proceeds under the offer from A$2.25 billion to A$2.57 billion, assuming the final price is within its indicative price range.

The total number of shares available under the offer will be between 1.12 billion and 1.28 billion, on the same assumption. ($1 = 1.0618 Australian Dollars) (Reporting By Jane Wardell; Editing by Paul Tait)