The investment would involve developing a proposed underground network to pipe heat from the city's recycling and energy recovery facility (RERF) to homes and businesses.
It is thought the project could benefit around 2,000 flats and public buildings.
Steam generated by the RERF would also be converted to hot water in a dedicated energy centre.
Hot water would then be fed into a 6.4km system of super-insulated steel pipes under the Aire Valley to heat properties along the route into the city centre.
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Heat mapping work has already been carried out to ensure the scheme is feasible.
Councillor Mark Dobson said: "A key benefit of the new recycling facility is the ability to deliver heat generated to homes and buildings.
"Not only could this help the city reduce its carbon emissions, it could help cut resident's fuel bills by around 10%.
"Such a significant investment will show that we are serious about making Leeds cleaner and greener and demonstrating that district heating networks are a viable source of low carbon heat."
A council contribution of £14m and a £7m bid under consideration by the Leeds City Region Enterprise Partnership, would allow the local authority to hire a design, build and operations partner.
Subject to a successful European funding bid, plans are in place to convert outdated electric storage heaters and replace older communal heating boilers at council multi-storey flats in Lincoln Green, Saxton Gardens and Ebor Gardens areas and connect them to the district heating network.
(LM/JP)
