Shropshire Council has applied to Historic England to seek 'immunity from listing' for Shrewsbury's Shirehall.
But, it has also emerged that the heritage guardians have also received two applications to confer listed status on the building.
Listed status could limit the ability to redevelop the site, hindering or preventing its sale entirely.
The council has confirmed it intends to leave the building entirely, with council leader Peter Nutting describing it as "no longer fit for purpose".
The consultation on all three applications closes on Friday and Historic England said that a decision on what happens will be taken by the Department for Digital, Culture, Media and Sport (DCMS)
Councillor Nutting said that immunity from listing would enable the council to get "best value" for the site and that given its key location in Shrewsbury the future uses need to be "flexible".
He said: "Shirehall is no longer fit for purpose for its current use. It generates around 1,044 tonnes of carbon per year and in the financial year 2019/20 running costs associated with the building were £1.3m, including £353,000 per year for gas and electricity.
"Last month, councillors agreed that the council will move out of Shirehall by 2023, and we now need to put in place plans in place to vacate and sell Shirehall, which will include determining the value of the site and the disposal/demolition cost.
"The site is a key gateway to Shrewsbury and it is important that we prepare the site for flexible use options for future uses to support the local area and the adjacent communities.
"As part of this work we have requested that Shirehall is granted a certificate of immunity from listing, which will enable the council to explore a range of future options and obtain the best value for the site.
"This would mitigate the risk of the building and site being left without occupiers and/or use for a prolonged period of time and In doing so add value to the public purse and maximising the amount of money that can be reinvested in front line services."
A spokesman for Historic England said: "We can confirm that Shropshire Council has applied for a Certificate of Immunity from Listing (COI) for the Shirehall, and we have also received two additional listing applications.
"These applications will be considered together. The case is out for consultation and that closes this Friday. Our advice will be formed and will go over to the Department for Digital, Culture, Media and Sport (DCMS) before the end of October. DCMS will make its decision on the case after that."
The Shirehall was built for Salop County Council between 1963 and 1966 to the designs of the County Architects’ Department, led by County Architect Ralph Crowe, with Alex Jeffries and assistants, and structural engineers Ove Arup and Partners.
Ove Arup and Partners have a significant role in architectural history having worked on a host of major projects, including the Sydney Opera House, London Zoo's famous penguin pool, and the Bird's Nest stadium in Beijing.