They have agreed terms on a deal to buy the club but will not proceed until they secure Selhurst Park, which is being sold by Bank of Scotland.
But a statement from CPFC 2010 on the Palace website says the deal presented by the bank is "unworkable".
CPFC 2010, a group of local businessmen headed by Palace fans Steve Parish and Martin Long, were named as the administrators' preferred bidders in March.
However, with the deadline to buy the club now looming, the Championship club could be no more if the consortium fails to reach an agreement to buy Selhurst Park.
We would urge the new Prime Minister to intervene personally to resolve the situation
CPFC 2010
The statement read: "We are trying to acquire both Crystal Palace Football Club and Selhurst Park.
"Everyone would agree Selhurst Park is pivotal to the long-term future of the club and CPFC 2010 have always made it clear they will not proceed without securing it.
"We reached what we thought was an agreement with Bank of Scotland, who are the major creditor of Selhurst Park Ltd.
"Subsequent to this agreement we have been sent a contract that does not reflect this agreement and is unworkable."
The sticking point in the negotiations appears to be over how much money the bank would receive if Selhurst Park was re-sold in the future.
Bank of Scotland have agreed to sell the ground to CPFC 2010 for a price lower that what a property developer may be prepared to pay but has asked for a share of any profit if it was sold again.
The consortium claim they have agreed to an "anti-embarrassment clause that allows the bank to see a further return if we realise greater value from the ground in the future."
The latest news is depressing and not good news at all. I hope something is done
CARL
However, the two parties now seem to disagree on how much that "further return" would be.
The statement continued: "It seems that the bank want to make an unlimited return in the future even if that value is created on the back of the success of the football club or money we have invested in a new infrastructure.
"We believe that the maximum they should make is the difference between what we will pay for the land as a football ground and what a property developer will pay now as a development opportunity plus interest."
The statement concludes by saying: "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."
Palace avoided relegation from the Championship on the final day of the season with a 2-2 draw at Sheffield Wednesday that condemned the Owls to League One.
The club currently does not have the money to pay its staff their wages for May and on Friday made 29 people redundant.
Fans were planning to hold a demonstration at Selhurst Park on Monday to highlight the club's plight.
Source: BBC Sport
Source: BBC Sport