The former Oceana nightclub building will be demolished in October and replaced with a new office block.
It forms part of the council's plans to transform the Kingsway into a business district.
The authority is moving from its seafront location as part of a wider regeneration of the city centre. Work is due to start in 2017.
The current civic centre site is likely to be replaced with public spaces, tourist attractions and homes.
Swansea council bought the Oceana building - which was once at the heart of the city's nightlife - in May and it is understood it has been earmarked as the potential new home for the civic centre and central library.
Demolition is due to take until March.
"Once we have control of that site we will look at the development and possibly start construction in 2016 to build offices which could be home for the council offices and Swansea library," said Swansea council leader Rob Stewart.
The building, originally constructed by the Rank Organisation in 1967 for a cinema, has accommodated a number of nightclubs over the years, including Ritzy and Icon, Time and Envy, and most recently, Oceana.
It also previously housed an Odeon cinema and Tesco before they were turned into a different club and bar respectively.
But it is no longer fit for purpose and a council move is one of a number of options being considered for the site.
The site which used to house Swansea's biggest nightclub could become the new home for Swansea council and library.