Many schools in the county were built in the same way as the County Hall extension
Part of Nottinghamshire County Council's headquarters could be demolished as it is "no longer needed" by the authority.
The building was designed by the Consortium of Local Authorities Special Programme (CLASP) in 1962 and spring-loaded to withstand mining subsidence.
Tim Gregory, the council's corporate director, said it was "old fashioned" and would cost about £9m to repair.
Bob Cullen from the Civic Society said it was an important modernist building.
He said: "I wouldn't call it ugly, I would say it's a building of its time but all buildings have a natural end.
"It's a CLASP building, a modernist building built to solve a particular problem."
Mr Gregory said the structure could be flattened if the council approved the plans.
He said: "It's very hot in the summer and cold in the winter... we don't need it anymore and would cost us a fortune to renovate it."
The prefabricated building was made with a series of steel frames and clad with concrete.
They were built spring-loaded as the windows of older structures would break when the coal board were sinking a new shaft.
Many of Nottinghamshire's schools, including the Kimberley School, were built in the same way.
The CLASP extension can be seen to the right of the main County Hall building
