Firms are being given until the start of May to submit prequalification documents for the two-stage design and build tender race.
The planned 100,000 sq ft centre will be built off Woodhouse Lane on a plot in the south east corner of the main campus.
Leeds University is looking for firms with a proven track record of delivering office and/or education projects in the last three years worth more than £15m.
The centre will drive innovation in technology-led companies and stimulate new high-tech firm start-ups by providing ready access to the University’s research and innovation.
The winning contractor is set to be revealed in October. Firms interested in bidding can obtain information at the University procurement site.
It is the smaller of two projects due to go out to tender. The University is also preparing to start tendering for a new £87m science and computing building at its city campus.
The North Eastern Quarter building will house the Bragg Centre for advanced materials and imaging and create new homes for the schools of computing and physics and astronomy.
Demolition of the former estates building and boiler house is anticipated for Autumn for a planned construction start in Spring 2017.
Under the present programme, the new building complex is due to be finished by 2019.