The revamp of Cardinal Newman Catholic School and Community College at the existing site will involve building a two-storey teaching block, sports hall and sixth form centre, as well as additional sports facilities.
The project in the Keresley area of the city could cost around £30m, subject to final price negotiations with the Department for Education.
BAM will carry-out the work, while the school remains operational, managing its team to ensure the efficient operation of the site and wider area.
The current school is designed for 1361 pupil places for ages 11-18 years old with 208 sixth form places.
Work is expected to start early next year on the site.