Antares Energy says it is open to talks with the US company seeking boardroom control of the Perth-based shale and oil gas play and promoting a five-point plan to double its share price.
Antares has advised shareholders it is considering its response to Lone Star Value's approach "having regard to the best interests of shareholders".
"This has included engaging with Lone Star with a view to obtaining clarity as to its intentions," it said.
Lone Star, an activist investor set up by one of billionaire investor George Soros' former fund managers, has used a newly acquired 5 per cent stake in Antares to requestion a shareholder meeting with the aim of dumping two of its four directors and appointing five nominees.
Antares shares last traded at 48Â¢, capitalising the group at $122 million. Lone Star, however, says the company is potentially worth between 81Â¢ and $1.49 a share.
It claims the group, which was criticised last year by proxy advisers, has been held back by a lack of board independence, poor investor communications and "excessive and poorly structured" executive pay.
Lone Star's plan for Antares includes the replacement of executive chairman James Cruickshank with an independent director, a US listing and a revised drilling strategy.
It said Antares was "at the crossroads", needing "decisive action and expertise" to increase value through "prudent expansion" of production "rather than go-for-broke as yet unfunded broad strokes".