RNC CEO Mark Selby told reporters yesterday the company would seek permission from the Australian government to take the specimens outside Australia on a world tour to build interest ahead of an auction.
However, he promised to bring them back.
Close argues the "extraordinary" stones are an important and significant part of Australia's heritage.
Close said the two largest specimens were each around 80% gold.
"The larger one - a 95kg mass containing an estimated 2440 troy ounces of gold - is, I believe, the biggest, most valuable, natural mass of gold existing today, while the smaller 63kg one contains some 1620 ounces," she said.
"It must be appreciated that these specimens have been mined underground in-situ and are not like rounded alluvial nuggets which are found near the surface."
Surbiton is a Melbourne-based gold consultancy and Close, a geologist, chairs the Heritage Committee of the Australasian Institute of Mining and Metallurgy.
RNC estimates it has pulled 30,000-35,000oz of gold from the Father's Day vein discovery.
Selby said he had received interest from museums regarding the specimens.
"These two amazing specimens are part of Australia's heritage and particularly Western Australia's heritage," Close said.
"They should be purchased by the Commonwealth and/or the WA state government and put on permanent display, to remind locals and overseas visitors of the enormous influence that gold has had on the development and settlement of this country."
Close suggested that displaying the specimens would also highlight the gold sector's important contribution to Australia.
However, she acknowledged the rocks were owned by RNC.
"The two outstanding specimens should be valued by a number of independent experts and then purchased at that valuation," Close said.
"They would make a wonderful exhibit and tourist attraction on display at, say, the Perth Mint."
Close said she would hate for the RNC specimens to go the same way as the Holtermann nugget, found in 1872 at Hill End, weighing around 290kg, standing 1.5m high and containing an estimated 3000oz of gold.
"Sadly, the Holtermann ‘nugget' was broken up, melted down and only a few rare photographs remain today," she said.
"Even though it was larger and contained more ounces than RNC's find, it contained only about 32% gold, compared with the estimated 80% gold content of the Beta Hunt specimens."
The RNC specimens are on display in Perth at the Precious Metals Investment Symposium.