Some of the industry’s biggest names will be vying for the job awarded under the Crown Commercial Service Construction Works and Associated Services framework.
The Enquirer understands the contract to rebuild the Terminal Car Park is worth up to £37.5m.
Interested firms attended a bidders day late last year and toured the site last week for a detailed look at the job with an initial tender deadline of this Friday.
The car park was destroyed last October when a major fire caused by a car suffering an electrical fault or leaking fuel line also damaged 1,300 vehicles.
Clearance of the structure and burnt-out cars has now been completed with the new car-park expected to open in late 2025.