The operators of Wirrimbirra Sanctuary at Bargo have received an eviction notice and told they must vacate the property and remove all of their animals by the start of October.
The Sanctuary, along Remembrance Drive, has existed since 1962 as an education and conservation facility.
Thousands of school children have visited the site on excursions during the past five decades.
The National Trust (NSW), the owner of the site, has found a new operator for the sanctuary.
The sanctuary's current operators, the David G. Stead Memorial Wild Life Research Foundation of Australia, plan to fight the eviction.
President of the foundation David Stead has called on the National Trust to reverse its decision.
"The state heritage-listed Wirrimbirra Sanctuary is one of Australia's first environmental education centres," he said.
"Today it remains a memorial to two of Australia's greatest environmental pioneers David G. Stead and Thistle Y. Harris Stead.
"If the National Trust succeeds in terminating the Stead Foundation's lease this will spell the end of a local environmental jewel."
The Stead Foundation's relationship with the National Trust has been strained for many years.
The National Trust could not confirm when it would announce the preferred candidate for the lease of the property.
A National Trust (NSW) spokeswoman said the organisation was planning for the future of the property at 3105 Remembrance Drive, Bargo.
"We will be entering into a new lease with the preferred candidate," she said.
"This candidate made their submission through the expression of interest process we commenced in 2018.
"The National Trust recognises the difficulty in re-housing some of the animals and on July 11 2019, we confirmed to the Stead Foundation that we will ensure the proper care of the animals should they remain at the property.
"The National Trust acknowledges the dedicated care given to the animals by the volunteers at the property over many years, and hopes their involvement will continue with the new tenants."
The National Trust spokeswoman confirmed the Bargo Dingo Sanctuary will remain at the property.
She also said the sanctuary would remain open to the public.
"The preferred candidate was selected on the basis of the proposed range of initiatives, activities and programs that will enhance the visitor experience at the property while continuing with education and research programs in the spirit of the founders of the property," the spokeswoman said.
"We understand the sanctuary is important in the local community and in the broader community.
"This is the very reason we conducted the expression of interest process over the last 12 months - to secure the best possible operators for the property, and to ensure it is maintained and sustained into the future."
A public meeting will be held at Wirrimbirra Sanctuary on Sunday, August 25 at 12pm to call on the National Trust to reverse its decision.
Former president of the Stead Foundation Margaret Kitson said the foundation had been 'betrayed' by the National Trust.
"Since 1965 the Stead Foundation have managed, fundraised for Wirrimbirra building accommodation, a visitors centre, native nursery, library as well as dams, gardens and memorials," she said.
"How can the National Trust have any credibility if it betrays one of Australia's most significant heritage places and oldest natural heritage organisations?"