Shropshire Council has operated the visitor attraction under a lease agreement for the past 40 years. However, visitor numbers have been falling and the council says it is having to subsidise the venue near Church Stretton.
It is currently closed to the public while a review over its future takes place.
Cecilia Motley, Shropshire Council cabinet member for culture, leisure and tourism, said: “We know the value people place on Acton Scott Historic Working Farm and we recognise its importance socially, educationally and in terms of the visitor economy.
“Our desire is to reach a workable solution with the estate and explore all possible options in doing so. This is of necessity taking some time, but we are committed to achieving a mutually satisfactory solution.”
The working farm museum was the vision of Thomas Acton who established a museum demonstrating farming techniques at the turn of the century before the advent of the internal combustion engine.
Visitor numbers peaked at around 45,000 in 2009 with the advent of the BBC’s ‘Victorian Farm’ television show and have now fallen to 20,000 visitors per annum.
The council says there is a current operating deficit of £168,000 per annum and says the Shropshire taxpayer has been subsidising the running costs of the farm at a cost of £8.40 per person.
Councillor Motley said: "Along with many other local authorities Shropshire Council is facing many additional pressures on its budgets. Regrettably the operation is no longer considered to be financially viable for the council.
“We really want to achieve an outcome that secures a sustainable future for Acton Scott Historic Working Farm.”
She said the review was wide-ranging as both parties wanted to be thorough in their evaluation to achieve a positive and fair outcome for Acton Scott Historic Working Farm.
A statement from the estate's owners says: "Shropshire Council has a lease agreement with the Acton Scott Estate which stipulates that the site should be run as a historic working farm, and we are obviously disappointed that the continuation of this arrangement is under threat. However, we do appreciate that Council resources are particularly constrained at this time."