Balfour Beatty, Bam Construct, Morgan Sindall, Skanska, Thomas Vale and Vinci have all submitted bids for the £20m first phase, according to information specialist Glenigan.
Developer Chatham Billingham (P & M) has employed Faithful + Gould as its agent on the project.
Phase 1 of the redevelopment will demolish the existing building and insert new levels into the existing basement volume to create an 800 space car park with a two storey building above.
The Phase 2 development will be a multi-storey building sitting above the car park. Outline consent has been obtained to establish the future height and massing of the building, which is expected to rise to 14-storeys.
