The Decent Homes programme saw 39,000 council properties renovated during the 2000s to bring them up to good living standards set by the Government.
But some tenants refused the work, leaving 2,932 homes in disrepair.
Sheffield City Council officers say that without improvements the properties will not meet national standards by 2026.
During the major refurbishment project the vast majority of houses, maisonettes and flats were given new kitchens, bathrooms, windows, doors, heating and electrics.
The council is hoping to re-engage with tenants who previously refused the work, according to the Local Democracy Reporting Service.
More stories from across Yorkshire
Paul Wood, cabinet member for neighbourhoods, said: “The council takes the quality of our social housing very seriously but tenants declined the work for a number of reasons including the inconvenience, because they had done their own improvements and because they were satisfied with the property at that time.
“Some works were not completed under the massive Decent Homes programme but this was the wish of the residents.
“Over the past few years some of these properties now require additional work to ensure the standards are maintained and we will deliver that for our tenants to ensure we have the best possible maintained stock in the UK.”
The council is looking for a contractor to deliver the work over an initial three-year period.
