The council is looking to appoint a contractor to refurbish the 11-storey development of the three linked 1960s blocks.
Wilmcote House, in the city’s Somerstown housing estate, contains 107 flats.
The council’s estimated cost is in the range of £10.5m to £12.5m. The aim is to start work in September 2013 and complete 18 months later.
For further details on how to bid for the work, see our Contract Leads section.