Community appeal for Dewsbury and Gomersal museums
Community groups have been asked to take over the running of two museum buildings in West Yorkshire, one of which had a £1m renovation in 2010.
The Grade II-listed Kirklees Museum in Crows Nest Park, Dewsbury, closed in November because of austerity cuts.
The Red House in Gomersal, which has close links to the Brontes, is due to close on Wednesday.
Kirklees Council said 30% of each building could be used for commercial ventures.
It is hoped community groups will come forward to run the buildings but, if not, they could be sold on the open market.
The council said any loaned objects will be returned to their owners or put in secure storage, while people who have permanently donated objects can be reassured they will remain in the care of Kirklees Museums and Galleries.
The reorganisation of the museum service is expected to save £531,000.
Councillor Graham Turner said: "We know the public support our plan to find new and innovative ways for them to view the collections.
"Museums are not just about buildings, it's about using the collections to tell the story of our past and how they influence what we do today."
The deadline for expressing interest or submitting an outline business case is 6 March and a decision will be made on 3 April.