East Anglian contractor RG Carter was this week due to be interviewed for the learning resource and heritage centre after making it on to a final list of three. The other shortlisted bidders are understood to be national firms.
Laing was due to be interviewed and the third bidder is rumoured to be either Bovis or Sir Robert McAlpine. Mace has also been linked with the project.
Industry sources said the scheme would be a major undertaking for Carter but that it is making a determined pitch based on its strong links with local suppliers.
None of the contractors or the client would comment on the final list, with a letter of intent for a winner due to be sent out on 22 March.
Cost certainty is an important aspect of the Michael Hopkins and Partners-designed project.
Project finance and administration manager Mike Delph said that, with a fixed, £30m grant from the Millennium Commission, the client had no option but to ask for a fixed price early. QS Turner & Townsend is advising it.
Delph said a form of contract is being drawn up to ensure cost certainty. This will involve a contractor giving a fixed price before entering a six-month "partnership" stage, during which it will work with the client on developing project buildability.
Once a contractor is chosen, civils and piling packages will be let separately. It is possible that a concrete and superstructure package will be let ahead of the contractor's second-stage appointment. This would leave the contractor to work on brickwork, glazing and roof elements.
Hopkins' competition-winning design will be built on a site adjacent to Norwich's main market square, which was occupied by a 1960s library before it burned down in 1994. The city council has granted the project client a 125-year lease.
There will be 120 000 books worth £10m transferred to the centre's library element, which will account for about 40% of the space. The project will also house 150 000 special items about Norfolk and a children's library.
It will also incorporate a business and learning centre organised with help from the local chamber of commerce, universities and the regional training and enterprise council.
A tourist information centre and a visitor centre with a heritage attraction on the history of Norwich and will also be included.