Developers are hoping to build 18 flats on land at the corner of Trinity Street, Furnace Hill and Copper Street on the Johnson and Allen car park.
The five to six storey building would include apartments, ground floor offices and basement car parking.
The land falls within Furnace Hill Conservation Area but there are no listed buildings. Slum clearance was carried out in the late 1920s and early 1930s and the area had been cleared of buildings by 1935. It was later levelled for a car park in 1962.
A report by the Archaeological Research and Consultancy at Sheffield University (ARCUS), on behalf of the developers, says the site used to have back-to-back and terraced housing arranged around a central courtyard.
'The streets were laid out on the line of old field boundaries and formed part of the early expansion of Sheffield in association with the increase in population in the mid 18th century,' says the report.
'During the 19th century, the area was perceived to be one of the worst slum areas in Sheffield due to the narrow street, poor sanitary conditions and proximity of industrial works to domestic housing.'
ARCUS says the site could hold clues to how our ancestors lived in the city.
'The lack of development at the area offers a significant opportunity for archaeological investigation of the late 18th century buildings.
'Domestic sites of this date in Sheffield have had little prior study and could provide important information on the living conditions of the working class in the 18th and 19th centuries.'
A heritage statement by SLA Design (UK) LLP says: Â 'The development proposal will satisfy an identified social and commercial need for this type of building in the area.
'The site is in a mix use residential and commercial area halfway up Furnace Hill. It is set on a corner towards the top of the hill surrounded by a mixture of residential apartments with commercial uses at ground floor level, factory /manufacturing units and offices. There is a distinct mixture of use types around the surrounding area.'
The plans have been submitted to Sheffield Council for consideration.