The consultation will question the public on their thoughts about Acton Scott Historic Working Farm, near Church Stretton.
The site, which has been operated by Shropshire Council for more than 40 years, has been closed to the public since last June after two cases of E-coli were discovered.
The council says it is "no longer considered a financially sustainable option", and that it is looking for "an alternative operating model".
Campaigners have started a group called the Friends of Acton Scott Museum, amid concerns that the situation could lead to the site being closed.
Since the closure last summer, the council has commissioned a number of reviews of the site including looking at health and safety, repairs and maintenance and staffing.
The authority said it has found "further staff training" and the need for "further investment in the site" had also been identified.
The council also said the attraction has been costing tax-payers around £168,000 a year since 2014, with visitor numbers declining.
A spokesman for the council said: "Regrettably, subsidising the site is no longer considered a financially sustainable option for Shropshire Council, particularly given the need for us to prioritise statutory services and publicly-owned venues.
"This may result in Shropshire Council no longer running Acton Scott Historic Farm.
"We're working with the Acton Scott Estate to find an alternative operating model that provides a sustainable future for the farm.
"We'll act as facilitator in collating community feedback and proposals. These will be passed on to the Acton Scott Estate to consider as possible alternative uses for the site."
The farm has previously featured in a number of television programmes and has been a popular venue for school trips and days out. It showcases traditional skills and highlights rare and native breeds.
Speaking earlier this month, Alice Walker, leader of the friends group, said: "Without places such as Acton Scott providing a venue, these skills would be at even greater risk of dying out."
She added: “The farm museum has educated and entertained for over 40 years and we see it thriving again in the future. It enjoys a great community atmosphere and has been a most successful tourist destination – until the pandemic.”
Shropshire Council is expected to use the results of the consultation for a decision on what to do with the site's future, with a report on the attraction to be considered by the authority's cabinet in the spring.
The consultation runs until March 14. To take part visit shropshire.gov.uk/get-involved/acton-scott-historic-working-farm-survey-2022