Construction work is due to start this summer and university staff are currently running the final rule over bids for the prestigious contract
Construction information specialist Glenigan said bidders include Ocon, Opl, Vinci and Graham.
University House was one of the first glass curtain walled buildings in the world when it was completed in 1963.
It will now be transformed into a new facility for students, staff and the community at the heart of the campus, as well as being integrated with the University’s Students’ Union.
The makeover has been designed by Sheffield based HLM architects.
Robert Smith, a fellow of the Royal Institute of British Architects, spent 12 years at the University from the late 1950s designing 11 buildings – including the Arts Tower and University House – while working for architecture firm Gollins, Melvin and Ward.
He said: “University House was designed to be a bit like the Arts Tower – it was a groundbreaking design. We were pioneers in glass curtain walling and this was one of the very first.
“It was a very fresh building design and very simple. It offered some of the best views of Sheffield, and still does now. It was designed to be unrestricted and benefited from not needing offices or room dividers so it was much more open than the other University buildings. We wanted to get as much light in as possible.”
Refurbishment work is expected to start on July 23 and finish in September 2013.