Radical Road was closed in 2018, amid fears for public safety following a 50-tonne rock fall.
While the agency is still considering “the most appropriate option” for the pathway with the help of specialists, it has not ruled out a permanent closure.
HES said: “The health and safety of our visitors and staff must always be paramount”.
In an “options appraisal” carried out by HES in 2021, which was released to The Ferret under freedom of information law, the agency found that a permanent closure would be the safest and most cost effective option.
It read: “A permanent closure of the Radical Road footpath would achieve the highest reduction in residual risk of injury to visitors and staff, and would allow Salisbury Crags to remain fundamentally unchanged, preserving the fabric and iconic setting within gates and high barriers,” the HES report said.
“Loss of this established footpath and the installation of permanent prohibition measures across all routes above and below the crags is likely to attract some negative public response.”
Before its closure, Radical Road’s path was popular with walkers and climbers. It was also famous for being the spot where Scottish geologist James Hutton found proof in the layers of rock that the Earth was much older than was previously believed.
Tour guides recently called on HES to allow people back onto the Radical Road footpath.
Nick Kempe, an access campaigner and author of Parkswatchscotland, said: "The Radical Road is one of the most historic paths in Scotland in what is an outstanding setting.
"Why is a world class tourism attraction still closed?"
Mr Kempe has urged MSPs to get involved to help solve the current access problem.
Ramblers Scotland outdoor group’s director, Brendan Paddy, told The Ferret: “It is sad and worrying to hear of the permanent threat to this iconic and historic path.
“We would urge decision-makers to carefully weigh any rockfall risk against the major negative impact of closure upon tourism and residents’ health and happiness.”
In response to The Ferret’s findings, a spokesperson for Historic Environment Scotland said: “We previously identified a risk of rockfall which could potentially cause death or serious injury on a section of the Radical Road and as a result were forced to restrict public access in this area.
“We continue to consult external specialist and partners on what is the most appropriate option to best remedy this situation, including discussions with relevant regulatory bodies to consider next moves in more detail.
“In the meantime, unfortunately access will remain closed. While it is never ideal or desirable to limit public access, and we acknowledge this area of the park has remained closed for some time now, the health and safety of our visitors and staff must always be paramount.”