Gold Coast, Australia-based Billabong said the party, which it didn't name, had offered "around A$1.45" per share and had signed a confidentiality agreement that enabled it to begin nonexclusive due diligence. TPG, which also offered A$1.45 per share, has been conducting due diligence since late July. Both approaches are conditional and nonbinding, and Billabong said it hopes the suitors will raise their offers after due diligence.

"As is the case for TPG's proposal, the Billabong board does not believe this proposal reflects the fundamental value of Billabong in the context of a change of control transaction," it said.

It added: "Billabong now considers that the interests of shareholders will be best served by a normal process to thoroughly evaluate whether a change of control offer, at a price and on terms that the board would recommend, can be secured."

Billabong representatives couldn't be reached and Bain Capital declined to comment.

Billabong shares in Sydney closed up 7.5% at A$1.365.

TPG on July 24 made a new approach to Billabong five months after Billabong's board, and its founder and leading shareholder, Gordon Merchant, had rejected a sweetened A$3.30 per share bid.

After TPG's unsuccessful February bid, Billabong replaced CEO Derek O'Neill with Launa Inman, former managing director of retailer Target Australia Pty. Ltd. It issued a profit warning and raised A$225.4 million in a heavily discounted share sale that increased the number of Billabong shares in issue by 86%.

Billabong, whose brands include Element, VonZipper, Honolua Surf Co. and Tigerlily, has also been closing stores to combat a sales downturn in Australia, Europe and Canada.

On Aug. 27, Billabong posted a net loss of A$275.6 million for the year ended June 30 because of exceptional items, with revenue down 7.9% at A$1.55 billion. Inman stressed that Billabong is profitable at the operating level and presented a turnaround strategy designed to increase 2012 pro forma Ebitda of A$84 million by 2.5 times over four years.

TPG has the backing of Colonial First State Investment Ltd. and Perennial Value Management Ltd., which together hold 12.5% of Billabong.

Under TPG's proposal, Merchant, who owns about 17% of the company, and Colette Paull, one of Billabong's earliest employees, would have the right to roll their shareholdings into a new vehicle. Both had opposed TPG's earlier approach, with Merchant calling in February for a bid worth more than A$4 per share. He has since publicly regretted that stance.

Bain, of Boston, last year bought private equity-owned business software maker MYOB Pty Ltd., of Sydney, for a reported A$1.2 billion after seeing off rival suitor Sage Group plc, of the U.K. For that acquisition, Bain turned to Morgan Stanley and law firms Ropes & Gray LLP and Clayton Utz for advice.

Billabong's advisers are Goldman, Sachs & Co. and law firm Allens.