The Roaches, near Leek is protected by national and European law because of the high conservation value of the landscape.
But the National Park Authority (NPA), which bought the 975-acre estate in 1980 to safeguard it from adverse development, is now looking for someone to buy the land.
The organisation is also considering working in partnership with another body to manage the site or letting it out on a long-term lease.
Adverts have been placed in estate and rural management trade magazines and interested parties have until July 30 to respond.
But Geoff Preston from The Ramblers Leek Group, said he did not think a buyer would be found easily.
He said: "I am surprised it is doing this. The estate was in private ownership until 1980.
"It was originally owned by the Brocklehurst family, as part of the Swythamley estate, but was sold off to farmers when the family died.
"They moved sheep on to the estate and there was an outcry.
"Then the NPA bought it and we thought its future would be permanently safeguarded."
Mr Preston said the Roaches was unique because of its Peak District views.
He said: "It is also one of the best climbing areas in the country.
"Unfortunately, places like this are becoming more difficult to manage.
"There is the cost of parking, maintenance, gates and signposts, and patrolling it."
Derek Rushton, from Ladydale, near Alton, was chairman of the Leek and District Field Clubwhich used The Roaches for walking for 53 years before the group broke up in October.
The 75-year-old said he did not mind the land being sold off, as long as it was managed properly.
He said: "As long as they keep the right of access to the public and don't charge for parking, it is fine by me.
"What we do not want is someone taking it on who would not be sympathetic to it being used by the public.
"I don't know who would buy it, though."
The estate is made up of moorland, farmland and woodland.
It also includes a car park at Gradbach and a cottage which is let to the British Mountaineering Council
The NPA said any deal would have to ensure that agreement continued.
Interested parties would also have to:
Ensure public access for recreation uses such as climbing and walking;
Manage the land to protect and improve wildlife, plants and flowers;
Work with community and recreation groups to develop a management plan for the estate and not allow shooting.
Roger Clarke, lead member for asset management at the Peak District National Park Authority, said: "We are putting guarantees in place as part of any agreement to ensure the Roaches remains a popular area for climbing and walking, as well as an important place for farming and encouraging wildlife, flowers and plants.
"We are looking to see whether there are other people and organisations who can help us deliver our objectives and bring resources to build on the significant improvements that have been made to the estate over the authority's period of ownership."
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