The leader of the Conservative-run Leicestershire County Council has asked David Cameron to designate the council as one of the government’s big society vanguard projects.
The moves comes after Liverpool City Council pulled out of the scheme in protest at public spending cuts earlier this month.
In a letter to the Prime Minister, Leicestershire County Council’s leader David Parsons says the council has spent nearly £2m on a programme to "build social capital" in the county over the past five years.
It says the council wants to ensure that "everyone has opportunities to influence decisions that affect them" and that local people can "shape and deliver" public services.
"Delivering big society in the current economic climate is a significant challenge, but it is a challenge that we fully intend to rise to in Leicestershire," the letter says. "I would therefore like to propose that you give consideration to including Leicestershire as one of your big society vanguard communities."
A statement from the council said it had set up a £350,000 budget that communities could spend on local priorities, and a £500,000 budget to encourage volunteering and community engagement.
Cameron launched the big society vanguard areas in Liverpool in July. The other areas are Eden Valley in Cumbria, Windsor and Maidenhead in Berkshire and the London borough of Sutton.
Joe Anderson, the Labour leader of Liverpool City Council, pulled out of the project earlier this month because he said cuts to the authority’s funding settlement from central government had "seriously undermined" the ability of Liverpool’s voluntary organisations to improve the quality of residents’ lives. He said the city had lost more than £100m of Area Based Grants, aimed at tackling deprivation, which had put some charities at risk of closure.
A spokeswoman for the Communities and Local Government department said: "The vanguards have been useful training grounds for the big society. We now have an open offer to all councils to work with them on specific initiatives like neighbourhood planning, and to bust bureaucratic barriers standing in the way of local action."