Derby MPs are urgently seeking further talks with the EFL in an attempt to break the deadlock that could force the Championship club into liquidation at the start of next month.
The Rams have until February 1 to demonstrate to the EFL they have the funds - thought to be about £5million - to complete the campaign.
In a sign of the growing crisis, the EFL, Derby's administrators Quantuma and Middlesbrough chairman Steve Gibson all released statements on Thursday, with the EFL claiming to be 'exasperated' that Quantuma 'have still not provided any guarantee of funds'. The governing body confirmed it had sought legal advice in an attempt to end the impasse.
Derby MPs have already met the EFL this week but are attempting to arrange another round of discussions as they try to find a route through the crisis.
One of the matters currently delaying a possible sale is compensation claims by Middlesbrough and Wycombe, who say they were directly affected by Derby's breach of spending rules. Derby qualified for the play-offs ahead of Boro in 2019, and avoided relegation at the expense of Wycombe last season.
But in a strongly-worded letter to Quantuma, Gibson said: 'We have no wish to see Derby County cease to exist. We only want to be dealt with fairly and can only conclude that you are currently choosing to use ourselves, the EFL and Wycombe Wanderers as scapegoats for your failure to conclude what should have been a relatively simple task of bringing Derby County out of administration.
'We hope that you will have the courtesy to respond to this open letter unlike our previous correspondence which remains unanswered.'
The EFL statement read: 'In an attempt to move this particular matter forward swiftly, the EFL has written to all parties with a proposed solution to negotiate a deal via independent legal mediation.
'By the Administrator's own forecasting, the Club will run out of cash by February, and therefore sourcing funds is of paramount importance to ensure they can compete for the rest of the season. This is when we have been informed the money runs out.'
Derby face local rivals Nottingham Forest on Saturday eight points adrift of safety, but off the bottom of the table despite having 21 points deducted earlier in the season.
They face further player sales in this transfer window unless more funding can be secured.
Quantuma remain hopeful of naming a preferred bidder in the coming days and have spoken to Rooney this week.
But they accept Derby could face further sanctions - likely to be a 15-point deduction - if an eventual new owner does not offer creditors the minimum settlement under EFL rules.
Their statement read: 'We have provided the EFL with 3 scenarios as to how that funding gap can be bridged and the EFL await further confirmation from us as to which scenario we plan to deliver. This will be dealt with over the next few days.
'We understand the frustrations of the supporters who are desperate for the club to survive and we are doing everything in our power to make this happen. We still believe a successful outcome is possible.'
Sportsmail revealed this week that Derby face oblivion unless they find about £5million to survive until the end of the season.
Several players have already left this month and a fire sale of assets - including academy talent - is being lined up to ease financial pressure.