Under the scheme householders would receive 50 pence for each kilogramme of waste reduced from its average waste levels but householders would only be able to receive a maximum of £17.50 a year.
The council could be the first local authority to pilot such a scheme. It has proposed that the trial lasts for six months, covering 2,362 properties on two refuse collection routes in Bishopston, Cothan and Redland.
If approved, householders will have to volunteer to be involved.
Bristol City Council executive member for the environment Cllr Gary Hopkins said: “We presented the bid for funding for this pilot and the panel of experts seemed very positive. We were certainly given no reason other than very positive that our bid will be accepted.”
According to the council, it was encouraged to formally propose the scheme to seek funding and support.
The proposal will be considered by a board including Defra, the Waste &Resources Action Programme and the Local Government Association which will then make recommendations to the Secretary of State. It will need to prove the pilot will benefit people and the environment, as well as providing useful data to inform future policy making.