Private health insurer NIB Holdings Ltd is hoping members of takeover target GMHBA will pressure its board to give a more serious consideration to NIB's $140 million offer.

Newcastle-based NIB has gone public with its proposal for GMHBA, after the board of the country's eighth largest health insurer rejected its takeover bid.

Geelong-based health fund GMHBA on Wednesday refused NIB's offer, citing it is neither compelling nor in the best interests of its members. The bid significantly undervalued GMHBA's business and the benefits and services that GMHBA members enjoyed, according to GMHBA chairman Ken Jarvis.

But NIB's managing director Mark Fitzgibbon argued "The offer price is very fair."

He said the merger would create a stronger company with 9 per cent market share, about half a million policy holders, and premium revenue of $1.2 billion, and that the offer includes a committment not to close any of GMHBA's retail centres and to open an NIB dental supercentre in Geelong.

While the board of GMHBA is refusing to further engage with NIB, Mr Fitzgibbon on Thursday called upon GMHBA to continue their talks.

"We hope to energise sufficient interest amongst the members of GMHBA and the local business community to say to the (GMHBA) board that this (offer) at the very least deserves more serious consideration than what you've given it," Mr Fitzgibbon said.

He said he hoped the GMHBA board would change its mind after proper scrutiny of the offer, and that NIB would continue to pursue GMHBA and talk to other health funds "because we believe in consolidation".

NIB, which is currently the nation's fifth largest health insurer, became the country's first health fund to demutualise and list on the stock exchange in 2007. The combined entity would be the fourth largest private health insurer in Australia.