The firms are believed to be tendering for the £25m first phase contract to build a new academic and energy centre at the Newton Park Campus.
Work could start as early as June if the University gets the planning go-ahead for the first phase of its ambitious plans for the campus.
Phase two of the project will involve the construction of residential accommodation for 600 students and the associated common spaces.
It is hoped that building work on the new residences will start in spring 2012.