Derby is bidding for £1.65m to build the city's first new council houses for 32 years.
The city council wants to get a slice of £450m of government money which has been earmarked for new council homes across the UK.
Cabinet member Bob Troup said: "With such a huge demand for social housing the possibility of building new council homes is an exciting prospect."
The council hopes to build 25 houses in Osmaston and eight in Chaddesden.
If the bid is successful, new residents could be living in the properties by summer 2011, the council said.
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