CPFC 2010, a group headed by local businessmen who want to buy the Championship club, said in a statement on Monday that unless they can complete a deal by Tuesday at 2pm GMT, the club would go into liquidation.
Although a deal had appeared to be imminent, a sticking point arose because one set of administrators are working with the consortium, and another are working on behalf of the Government-owned Bank of Scotland, who own the club's Selhurst Park ground, and are its major creditor.
CPFC 2010 have appealed to the Prime Minister, whose new coalition government is committed to sport, to step in and prevent the Bank of Scotland overseeing its demise.
"As we sit today the future of Crystal Palace hangs in the balance and is very much in the hands of a person in a bank in Scotland whom we have never met and, it seems, we are not allowed to speak to.
"We note the new government's commitment to sport, particularly sport in the community. Bank of Scotland is currently government owned.
"As such we would urge the new Prime Minister to intervene personally to resolve the situation or see a club supported by many thousands, and with a 100-year history, consigned to the scrapheap," the statement on Crystal Palace's official website said.
Palace, formed in 1905, have had four spells in the Premier League and reached the FA Cup final in 1990, losing to Manchester United in a replay.
They avoided relegation to League One on the final day of the season when a 2-2 draw with Sheffield Wednesday sent Wednesday down instead.
