Leeds City Council said Calverley Library could be re-developed after it is put up for sale by public auction.
Library services provided at the Thornhill Street building, built in 1973, are set to move to Calverley Mechanics Institute.
A council report said the sale would raise cash for the authority, which must make more than £100m in savings this financial year.
It said: “The building is located in the centre of established residential area.
“It is likely the building will attract a number of buyers from self-builds and builders to demolish and redevelop.”
More than £200,000 was being invested in a refurbishment of the nearby Mechanics building to make the re-location possible.
The council said it was liable for maintenance costs while the current building was still in use.
The report said: “A disposal will remove these responsibilities and associated costs.”
The council said it held a detailed public consultation on the future of the library service.
The report said: “It should be noted that a mobile library service will be utilised during the relocation of library resources to the Mechanics Institute.
“This is to ensure continuity of service and minimise any down time.”
The council said it was proposing to sell the library building before the end of this financial year.