The Fashion Museum in Bath could close for three years after being evicted from its current home.
It had been at the Assembly Rooms since 1963 but it is being forced to move to make way for a new heritage experience.
The National Trust, which owns the building, plans to create an 'immersive experience' celebrating the city's Georgian history.
Bath and North East Somerset Council said it may not be able to relocate the museum for another five years.
The National Trust is enforcing a break clause on the Assembly Rooms, forcing the attraction to leave its underground site in March 2023.
The collection of over 100,000 items will be put into storage if a new home cannot be found, the Local Democracy Reporting Service said.
Bath and North East Somerset Council, that runs the museum, said it wants to identify a highly visible, central site with a flexible exhibition space and a dedicated learning area.
It also wants to create a collections centre to enable important items to be loaned to prestigious exhibitions elsewhere.
In 2019, more than a million people saw pieces from its collections in London, New York, Vienna, Bruges and Bendigo, Australia.
A council report said the museum's "underground position, in a non-central location with no on-street identity, is no longer adequate for an institution of this standing".
However, the report suggested that a new site may not be ready to open before 2026.
Cabinet members will consider the plan on Thursday, 20 May.