The council is looking at options to sell the landmark building for a £35m redevelopment into offices or a hotel, or alternatively sell a long lease and refurbish the building to keep it in council use.
The building was listed in 2007 by the Department of Culture, Media and Sport against the council’s wishes, scuppering plans to demolish it and redevelop the site.
English Heritage has recognised Plymouth as one of the best examples of post-war town planning in the country with the city boasting the highest number of post-war listed buildings outside London.
The council hopes to find a developer to carry out the estimated £35m revamp plan by next year and has issued an OJEU notice.