The new bid is valued around A$694m (£448m) and matches an existing bid from private equity suitor TPG Capital.
Billabong said a new party offered “around A$1.45” a share and has signed a confidentiality agreement and been granted due diligence.
Sources who declined to be named have identified the fresh suitor as Bain Capital.
US-based TPG Capital offered A$1.45 per share for Billabong on 24 July, and said it could raise or lower its price after it has seen Billabong’s books.
Billabong’s board said it did not think either proposal reflected the fundamental value of the company.
Both of the offers are indicative, non-binding and conditional, and the offer price may be refined after perusal of Billabong’s books.
Billabong spokesmen declined to comment on the bidder’s identity.