The construction cost is estimated £20m, exclusive of the university’s direct fitting-out works.
Bam, Kier, Miller, Shepherd and Vinci expect to hear whether they are the winning bidder early next year to allow work to start in the spring.
Fit-out firms will move in under separate contracts in April 2015.
The school will be the first in the South East outside London and includes a main academic centre with offices, teaching spaces, lecture theatres, and labs.