Built in 1852, Kilns House – which sits between the current municipal buildings and Dollar Park – has lain vacant for several years and is now in a poor state of repair.
The council says the B-listed, red sandstone villa is in need of significant refurbishment, and is no longer fit for purpose or of use to it.
It is proposing that Kilns House and a large part of its ground should be advertised and sold.
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However, a significant area, which allows pedestrian access from the town centre to Dollar Park, will be maintained.
Selling the house and garden could allow a developer to restore the building, either creating a small hotel – or another commercial enterprise – or converting it into homes.
However, as the building was bought by the former burgh of Falkirk in 1954, it belongs to the Common Good Fund – and that means residents of the old burgh must be given a say in its disposal.
A consultation is now open and it will run until April 14.
A spokesperson for Falkirk Council said: “We’re really interested to receive a wide range of thoughts from the public about the potential future of Kilns House.
“Given its architectural importance as well its stunning location, it’s important that views are taken on board prior to releasing it to the market.”
The wider area of Kilns was originally part of a large estate belonging to the Nimmos – the family who also owned Westbank, the mansion that was eventually demolished to make way for the current municipal buildings.
The Nimmos sold part of their land to the then Procurator Fiscal of East Stirlingshire, John Gair, who built the current house there in 1852.
Her died at Kilns on April 14, 1891, but Mrs Gair and her daughters continued to live there and the connection with the family was not severed until Miss CL Gair – the last of John Gair’s children – died in April 1932.
It was bought by Falkirk solicitor, Thomas Graham Marr, who owned it until May 1954.