The 1940s work Figure Study II was given to Batley by the Contemporary Art Society decades ago.
But recently, apart from occasions when it has been taken on art tours around the world, the canvass has mostly been stashed in the vaults of Huddersfield Art Gallery.
Experts suggest that the piece could now worth a whopping £60m – the same amount that Kirklees Council spends on supporting children and families – but insurance costs are apparently too high to put it on display in Batley.
Council leader David Sheard has started a debate about whether the work should be sold to benefit public services in the district.
The Labour councillor for Heckmondwike posted online: “I have been asked ‘Should we sell our Bacon. Any thoughts?”
He added: “If I were a philistine, I might compare the costs of caring for a piece of coloured canvass to an ageing resident with dementia.”
But Malcolm Haigh, chairman of the Batley History Group, said: “Instead of it being hidden away, why not sell it with the provision that the money that it fetches is spent in Batley.”
He said that the cash could benefit cultural venues such as Batley’s town hall, which has had much of its services slashed or moved due to cuts.
“There would need to be an agreement that it’s not spent elsewhere,” he said.
Mark Griffin, who runs community interest company Batley Smile, said he would like to see the work retained to promote the area, or given to a trust which could make sure the town reaps the benefits from its use.
He said: “In Kirklees’ art collection there’s nothing that touches this in terms of value.”
But he added: “It’s a one off. You don’t get the money again.
“There’s great value in promoting that painting for the benefit of Batley and renting it out.
“I would rather see it retained and promoted really positively.”
Irish-born Bacon, who was celebrated for his grotesque imagery, died in 1992, since when the value of his works have rocketed.
But selling from public collections is frowned upon in the art world, where it is often thought of as betraying the donator and dissuading people from gifting works in the future.