Suffolk County Council plans to stop its funding for 21 country parks and picnic sites, cutting £415,000 from the 2011/12 budget.
Councillor Judy Terry, cabinet member at the Conservative-led council, said: "It is an exciting opportunity for local people to develop the sites."
The cuts would save 57.9% from the existing country parks budget of £717,000.
Ms Terry said the public would continue to have access to the sites.
The county council is proposing to save a total of £42.5m from next year's overall budget.
This represents a cut of 8.4%, but does not include the education budget, which is funded by a separate grant from central government.
Ms Terry said that any site which does not get taken over would remain open, but would probably lose facilities such as toilets and run at "low maintenance".
The council is seeking "firm expressions of interest" from those looking to take over the sites by the end of March.
Alan Anstead, from the campaign group Save Suffolk's Country Parks, said he was worried the council was acting too quickly.
"I think they have to go a bit slower," he said.
"They have to allow some money next year for maintenance and so this process can be done in a proper way that gives people the chance and time to put together good project proposals.
"We want a guarantee from Suffolk County Council that they won't close the parks, or sell them to a private organisation that will keep them closed to public use."
Suffolk County Council is voting on its 2011/12 budget on Thursday.
The affected sites are:
- Barham Picnic Site
- Bawdsey/Felixstowe Jetties
- Bawdsey Quay Huts
- Belstead Meadows, Ipswich
- Bramford Meadow Nature Reserve
- Bramford Picnic Site
- Brandon Country Park
- Cattawade Picnic Site, Brantham
- Clare Castle Country Park
- East Lane Car Park, Bawdsey
- Fen Alder Carr, Local Nature Reserve, Creeting
- Greyfriars, Dunwich
- Haughley Picnic Site
- Knettishall Heath Country Park
- Lavenham Walk
- Melford Walk
- Ramparts Field Picnic Site, Icklingham
- Rodbridge Picnic Site, Long Melford
- Toby's Walks Picnic Site, Blythburgh
- Valley Walk, Sudbury to Long Melford
BBC Suffolk's Any Suffolk Questions? programme looking at county council cuts is broadcast at 1800-1900 GMT on Wednesday, 16 February.