Rangers wish to delay a decision on Craig Whyte's takeover because of doubts about the level of investment and to consider an alternative.
Whyte wanted to close the deal to buy Sir David Murray's majority shareholding on Monday.
But chairman Alastair Johnston said the board did not wish to be "pressed into an unrealistic timescale".
"We have had an approach from a director who wishes us to consider an alternative funding option," he said.
And it is believed that financial consultant Dave King and fellow director Paul Murray are the men behind the new plan to raise £25m to pay off their debt owed to Lloyds Bank and provide funding for the squad next season.
Johnston's statement via Rangers' website came 24 hours after the Whyte camp told BBC Scotland of their frustration at the board's desire to delay a decision until the end of the season.
The chairman is believed to be unhappy that this had been made public but has now gone on record to explain the position of the board's independent sub-committee.
"For some time, the board has had major concerns about its engagement in the process," said Johnston.
"After nearly six months of negotiation, we have only very recently had the opportunity to meet Craig Whyte and his team.
"Moreover, it is only in the last few days that we have started to receive the draft agreements outlining the transaction, although we are still awaiting a detailed working capital statement demonstrating that there is sufficient funding in place to meet the pressing needs of the club.
"Based on the documents we have only been able to review within the last week, we are disappointed that they ultimately did not reflect the investment in the club that we were led to believe for the last few months would be a commitment in the purchase agreement.
"Given the requirement to repay the bank in full under the proposed transaction, there appears to be only a relatively modest amount of money available that would positively impact the club's operations, especially as it relates to an urgent requirement to replenish and upgrade the playing squad.
"Whilst the proposed transaction has addressed the interests of Lloyds Bank, the Murray Group and Craig Whyte, our perspective is solely directed towards the future of Rangers Football Club.
"We have legal responsibilities to ensure that the proposed transaction serves the best interests of the 26,400 minority shareholders, many of whom are season ticket holders."
Whyte has been in negotiations to buy Rangers since mid-November and sources close to the Scottish businessman recently suggested that he had decided to make available "significantly more" than the £25m over five seasons he originally earmarked to strengthen the playing squad should he take charge.
However, Johnston said that one of the club directors had suggested an alternative way to improve the cash-strapped club's finances.
"This would involve a fresh issue of new capital to raise £25m to be invested directly into the club," stated the chairman.
"The board believes that it has a responsibility to examine this proposal whilst continuing its review of the Craig Whyte transaction.
"On Monday, I had a lengthy conversation with Craig Whyte explaining the dilemma that the board now faces.
"It was a constructive and healthy dialogue and, whilst he expressed his frustration, he understood our position.
"We agreed to remain in touch in terms of working towards a resolution that is in the best interests of all parties involved as we receive more information relating to his financial commitment to Rangers Football Club."
The independent committee was set up to examine the credentials of potential buyers and includes Johnston and chief executive Martin Bain, as well as John McClelland, Donald McIntyre and former player and manager John Greig.
A source close to Whyte claimed the board's move made "no sense at all" and was "clearly a misguided attempt to further delay or disrupt the deal".
"For a start, the deal Craig Whyte is putting forward is worth £52.5m, more than double the amount apparently to be raised by this unnamed Rangers director.
"Further, the Craig Whyte investment in the club would begin on day one of a deal being completed.
"Most importantly, it would mean that the debt owed to LBG would be cleared, which has been one of the key demands of the entire deal."
The source added that proof of funds had been given to the Murray International Holdings and Lloyds.
"This means that not only will debt be repaid immediately but that £10m will go into Rangers' bank account on the first day as working capital," he added.
"Any contrary suggestion about funding is not only untrue but also defamatory.
"There is no certainty that this new proposal has any likelihood of success, whereas the deal being put forward by Craig Whyte is real, it can happen immediately and will help secure the future of Rangers FC at a time when it faces great uncertainty.
"The proposed Craig Whyte deal has been has been fully accepted and agreed by both Murray International Holdings as the principal shareholder in Rangers FC and the Lloyds Banking Group as the right deal for Rangers.
"It appears to be only one or two members of the current Rangers board who seem intent on delaying this deal and, if that happens and the deal collapses, that will be very bad news for Rangers and the loyal fans who deserve better."