The 300-year-old cottage, which includes the museum, is offered for Asch 4.5m (pounds 292,000) in the property advertisements of the Spectator this week. But the local council says it has no statutory right to enforce the new owners to keep the museum open.
Auden, the most influential English poet of his generation, moved to Kirchstetten after a hunt during the late Fifties for a home within reach of the Austrian opera houses.
The poet, who died in 1973, bought the house in 1957 for 120,000 schillings (pounds 3,000 sterling), and the existing furniture and fittings for another 25,000 schillings. He moved into the 18th-century former farmhouse with his long-time companion Chester Kallman and three cats, two goats, one pig, two hens and 173 goldfish. His biographer, Humphrey Carpenter, quotes him as saying: "I am enchanted and so is Chester with our Austrian house. It's just like Beatrix Potter."
A sequence of Auden's poems, About The House, was inspired by Kirchstetten, including The Cave of Making (his study), Down There (the cellar) and the Cave of Nakedness (his bedroom).
He summed up his feelings in In Thanksgiving for a Habitat, where he notes "what I dared not hope or fight for/is in my fifties, mine... where I needn't ever be at home to/those I am not at home with, not a...windowless grave, but a place/ I may go both in and out of."
The present owner, Franz Strobl, the son of Auden's last housekeeper, bought the house from Kallman in 1973.
He and his wife, Brigitte, are selling up because the house is too big for them.
Two rooms are preserved as a museum to Auden, for which the local authority pays rent of Asch8,000 a month. It is not a formal museum, and Auden acolytes must ring Frau Strobl to check she is in before they visit.
Maria Rollenitz, responsible for cultural affairs on the village council, said the authority had no statutory control over who bought the house: "But we would very much hope we will be able to continue opening it to visitors."
Kate Bucknell, a founder of the Auden Society, said the potential loss was sad but not a tragedy: "The places in Auden's literary career were important to him and they can be seen as geographical monuments - The Pennines, Kirchstetten and New York - but it's not necessary to institutionalise them."
But David Luke, a friend who visited Auden several times at the house, said: "If the house isn't associated with Auden in the future, commemorating him, it's a great pity and I'll be very surprised."Reuse content