Bury Council, in Greater Manchester, said it was considering selling the artwork to help it pay off a deficit of about £10m.
The painting - A Riverbank - is currently on public show at the town's art gallery.
The council blamed the proposed sale on it receiving less money from the government than it had expected.
Chief executive Mark Sanders said he was "hopeful" the painting would remain available to the public if it was sold.
Reinvest money
He added: "The painting was bought many years ago for the princely sum of £175.
"It is not central to our collection, which centres entirely around Victoriana, and we need to reinvest that money into services."
The move was expected to be approved at a council budget meeting on Wednesday evening.
Also among the proposals are to raise council tax by 5% so an average Band D property would be charged more than £1,200.
Other plans include raising parking fees, reducing the amount of road maintenance and cutting opening hours at the borough's art gallery and libraries.
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