Wandsworth Town library, which opened in 2009 following a £1.5m redevelopment, could be relocated under new proposals.
The council wants to move the library from the grade II listed former court house, 11 Garratt Lane, to a new building next door, with plans to put the former on the open market - potentially to a restaurant.
The library opened four years ago, to much fanfare, following a £1.5m redevelopment funded by Wandsworth Council.
The council said more than 1,600 people visited the new library on the first day it opened with Councillor Sarah McDermott saying they had been inundated with compliments about the look and feel of the building.
She said at the time: "The glazed wall is particularly popular; it really floods the rooms with light and creates a bright and inviting atmosphere.
"We expect this building to become one of the busiest libraries in the borough and a real asset to the residents of Wandsworth town centre."
If the library is moved the council is likely to have reduce running costs, annual revenue savings and an income from renting out the old site, according to a report by the finance and corporate resources overview and scrutiny committee.
The report also said there would be no interruption of library services if it is relocated.
The proposed new library would adjoin the old burial ground, would be located opposite Southside Shopping Centre, on two floors and operational by 2018 or 2019.
A spokesman for Wandsworth Council said: "The council has drawn up joint proposals with South Thames College for a wide scale regeneration project that will involve the replacement of a number of 1960s office blocks with attractive and modern new buildings providing homes, office and retail space, improved educational facilities, a new public square and a brand new public library.
"The creation of a purpose-built and better library means that it may be able to host its own coffee shop, which we think will add to its popularity and hopefully ensure greater visitor numbers.
"The plans also call for the opening up of the old burial ground in Garratt Lane to provide a much more accessible and welcoming green space in the heart of the town centre."
The report indicates provisional fit-out costs at £230,000 for the library and £100,000 for a lift. IT costs are yet to be estimated.
The news comes amidst concerns for the future of the borough's libraries after a private and confidential Conservative Party document was leaked to the Wandsworth Guardian revealing a number of proposed savings, including "consideration of closure of non-town centre libraries".
Wandsworth Council leader Ravi Govindia said there were absolutely no plans to close any library in the borough.
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