The proposed 60,000 sq ft engineering building will be constructed in two or three stages.
The building will include research, teaching, office and communal spaces along with laboratories.
It will be developed to RIBA Work Stage D by an architect, still to be appointed, at which point designs will be novated to the winning bidder.
Documents and expressions of interest are due 10 November through the University’s procurement portal.
GB Building is presently working on a £14m sports and leisure facility for the University, which is due for completion in April next year.
Leeds architect Watson Batty designed the new complex.