A steering group was formed when the park, off Old Hunstanton Road, went on the market for £500,000 in April.
Members lobbied the parish council tonight, asking it to back them financially.
Villager Mark Pishorn told the meeting, at the Jubilee Clinic: 'We want you to back us if we put a bid on that park, either the whole thing or whatever's left to buy, meaning you'll back us on any financial shortfall in the future.'
Council chairman Peter Colville said a meeting would be held as soon as possible. He added: 'Whatever the council's decision, I'd like to commend you all on your efforts and enthusiasm for this park project.'
A public meeting on Sunday heard there were potential buyers interested in two of the three separate lots of land which make up the park, while pledges of financial help totalled just £27,500.
Villagers voted to lobby the council, to ask it to borrow the money to buy the site, putting up council tax bills by 69p a week to pay off the loan. They hope to preserve the 44-acre park, the village's last significant green space, for future generations.
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