Trustees of a pottery exhibition in Stoke-on-Trent are worried that spending cuts will lead to its closure.
The cit council is proposing to stop funding costs to Ceramica in Burslem, a display looking at the past and future of the pottery industry.
Manager Karen Burgess said mothballing it would "not improve the look of the town".
Councillor Hazel Lyth said it was a shame but the council had to concentrate on what was important.
Ceramica is based in Burslem's former town hall.
Ms Burgess said it would be very sad if hoardings had to be put around the building to protect it if Ceramica left.
"It is grade II* listed," she said.
"I also think it sends out a negative impression of the hopes of the regeneration of the town".
Councillor Lyth, portfolio holder for culture on the Labour-led coalition council, said: "It is a sad story in some senses but we've got to do the things that we must do."
The matter will be discussed at a full council meeting on 24 February.