UPDATE 3-Kirin makes buy-out approach for brewer Lion Nathan

* Kirin owns 46.1 pct, rest worth at least $1.7 billion

* Kirin chases a piece of Australia's beer duopoly

* Kirin shares up 3.6 pct; Foster's, CCA also buoyed (Adds analyst and investor comment and detail)

By Simone Giuliani and Taiga Uranaka

MELBOURNE/TOKYO, April 23 (Reuters) - Japanese brewer Kirin Holdings (2503.T) is seeking a buy out of Australia's No.2 brewer, Lion Nathan Ltd LNN.AX, in a deal shareholders said could be worth at least A$3.3 billion ($2.3 billion).

The high-margin Australian market, which operates as a duopoly between Foster's Brewing Group Ltd (FGL.AX) and Lion Nathan, has long been cited as appealing to Japanese brewers who have been looking to expand beyond a shrinking home market.

It has also become more affordable since Australia's dollar shed a third of its value against the yen in the last 10 months.

Lion Nathan, the maker of XXXX Gold and Hahn beer, said Kirin had made an approach for the 53.9 percent of shares it doesn't already own. No price was given, but analysts said history demonstrated that Japanese brewers can offer generous premiums.

Analysts and investors pointed to the A$11.50 a share Kirin offered to pay for Lion Nathan shares as part of the funding Lion needed for a failed A$7.6 billion bid for Australian bottler Coca-Cola Amatil Ltd (CCL.AX) last year.