Pictures: Michael Gillen
The building is leased from West Lothian Council by the Heritage Trust and houses the town’s museum.
However, with a move planned to the new Linlithgow Partnership, Annet House will no longer be needed.
The local authority has made it clear that as it prepares to make £73 million of cuts in the next five years, it will be looking to sell off any assets deemed surplus to requirements.
But a petition asking the council not to sell the building and, in particular, its historic gardens, has been launched by Clare Rainey.
She said: “Wouldn’t it be great to get together as a community and save this wonderful resource so that we could use it to the benefit of all?”
On Tuesday the impending sale is due to be discussed at a meeting of Linlithgow and Linlithgow Bridge Community Council, which takes place in the Burgh Halls education room from 7.30pm.
Annet House is a Georgian townhouse built for merchant George Bartholomew in 1737 and is the last remaining terraced ‘rigg’ garden in the area.
The museum is not expected to move into the partnership centre before the end of 2018, giving campaigners time to consider how to safeguard its current home.