Gordon Stewart is one of only four people to have submitted a formal proposal to the New Zealand Geographic Board to name a geographical feature after Sir Edmund.
Mr Stewart, a Cromwell Community Board member, said he has the support of Sir Edmund's widow, Lady Hillary, who suggested the peak could be called Hillary Peak.
"Thank you and good luck with the proposal," she wrote in March last year.
Following the death of Sir Edmund in January 2008 aged 88, Mr Stewart decided to gauge public opinion and proceed with an application to name what is believed to be the highest unnamed peak in the country after Sir Edmund.
The unnamed Hector mountain peak, locally referred to as "top peak" or "cone peak", is believed to be the highest unnamed peak at 2307m in the country, he said.
Although the peak, which can be seen from Cromwell, did not have any significance to Sir Edmund, it would be an honour to name a peak in the area after him, Mr Stewart said.
"I had the pleasure of meeting Sir Edmund in Nepal in 1991 and I believe he was the most outstanding New Zealander. It would be an honour to name a peak in the area after him."
With another unnamed peak nearby, at 2252m, Mr Stewart has suggested it could be named after Tenzing Norgay, the sherpa who along with Sir Edmund became the first to climb Mt Everest in 1953.
More than 79 people supported his idea with only four submissions against, and it is now one of three formal proposals in front of the New Zealand Geographic Board, after a move to change Mt Aspiring/Tititea was declined by the board last year.
The other formal nominations are the Southern Alps (the Hillary Alps, the Edmund Hillary Alps or the Hillary-Everest Alps) and an unnamed mountain in the Two Thumb Range (Mt Ed Hillary), near Fairlie.
Geographic board secretary Wendy Shaw said a number of people had approached it seeking to name New Zealand geographical features in honour of Sir Edmund.
"The board is fully supportive of such suggestions, and is confident an appropriate feature can be identified and officially named."
Two Antarctic geographic features were named after Sir Edmund while he was still alive, including the Hillary Coast, south of Ross Island, and the Hillary Canyon, an undersea feature in the Ross Sea.
The board has agreed to defer any considerations of proposals until at least two years after the anniversary of his death.
Te Runanga o Ngai Tahu were aware of "a number of proposals" to rename geographic features in honour of Sir Edmund, kaiwhakahaere (chairman) Mark Solomon said.
"At this stage there has been no formal discussion with the New Zealand Geographic Board about any of these proposals. Ngai Tahu is one of a number of groups that are consulted in these cases and will consider each proposal on its merits."
The closing date for nominations is likely to be early 2010 when the board will meet and notify the public of its preferred proposal, after which it will be open to the public for consultation.
