Hove Library faces closure under a plan that will cost £190,000 more than keeping it open.
The library, opened in 1908 after donations by millionaire philanthropist Andrew Carnegie, is in desperate need of renovation to meet new government standards.
Brighton and Hove City Council last year agreed to spend more than £400,000 to upgrade facilities, including the installation of a disabled access lift.
However, the minority ruling Labour group now believes it best to transfer the library to Hove Town Hall, even though that would cost £590,000.
A similar suggestion was ruled out by the council two years ago on the grounds that it would cost more and would be unpopular.
In November 2001, the then-culture director Sarah Tanburn said: "Moving the facility would be unpopular as the existing purpose-built library is loved by local people."
Now council chiefs argue the proposed modernisation of the original building in Church Road is not possible and that the town hall would be more convenient for users.
Other political groups will be consulted before a decision is made at the council's policy meeting on October 22.
If the transfer is agreed, the public will be consulted on the best way to handle the move and what should be in the new library.
Head of libraries Sally McMahon said staff were in favour of the move because conditions would be far better for them and for visitors.
The transfer proposals would involve taking over the banqueting room in the town hall, which would offer twice as much space as in the present building.
It is also feared the Disability Discrimination Act, due to come into effect next year, would sharply reduce available space in the old building.
The new library would be fully accessible for disabled people and would allow lower running costs and longer opening hours because fewer staff would be needed to supervise it.
It could also include a meeting room, a cafe and a corner for teenagers in addition to a children's library.
Deputy council leader Sue John said the Church Road building was impractical because it was on many different levels, not all served by a lift for people with mobility problems, and the library suffered from damp.
She regretted the loss of the old building but said it was "not practical".
If the library was closed it would be sold but could not be demolished because it is a listed building.
Conservative group leader Brian Oxley said: "I'm disappointed Labour should have come to this conclusion without putting it to the other groups."
Liberal Democrat group leader Paul Elgood said: "We have very real concerns about the loss of this building which has been at the centre of the Hove community life for nearly 100 years.
"It is a much-loved building and it wouldn't take much to bring it back to life again, even though it has been neglected."
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