Former Ibrox director Paul Murray's group announced it was stepping back from the proposed takeover of the crisis-hit club after it emerged consortium partner Ticketus was attempting to strike a deal with a rival from Singapore.
It appears to put the offer, fronted by businessman Bill Ng, in pole position to become the preferred bidder for the stricken club later this week.
However, the deal they are believed to be brokering with Ticketus was described by one Blue Knights source as "not in the best long-term interests of the club".
It is understood that the third bidder, American Bill Miller, is almost out of contention.
But there is deep anger within the Blue Knights at the tactics deployed by London-based Ticketus, which originally aligned itself as part of the consortium comprising Paul Murray and three supporters groups.
The Blue Knights said they had been asked by Duff & Phelps to reconfirm its best and final offer on Thursday, believing that the following day this would lead them to being named preferred bidders.
The administrators requested the group provide a non-refundable deposit as part of the process. Ticketus decided it did not wish to provide it, said the Blue Knights.
In a statement, the consortium said it was made aware over the weekend that "Ticketus had been in discussions with the Singaporean consortium who, on Friday, had offered Ticketus a substantially better deal to the one offered by us. We confirmed that we were not prepared to increase our offer to Ticketus".
The statement added: "The consortium believes that the whole deal process has now become incredibly complex and it is critical that a preferred bidder is appointed this week.
"As a consequence, in the best interests of the club, the consortium has decided to take a step back to enable Duff & Phelps, Ticketus and the Singaporeans to conclude a deal as quickly as possible.
"We stand ready to complete our offer of April 4 which included a deal in principle with Ticketus."
The Blue Knights reiterated that their deal, with Ticketus on board, "represents the best opportunity" for Rangers to exit administration via a Company Voluntary Arrangement (CVA).
The decision to involve Ticketus as a Blue Knights partner had strengthened the bid led by Mr Murray. It removed Ticketus, and the £27 million it is owed as part of a four-year season ticket deal struck by owner Craig Whyte, from the list of creditors in a CVA.
The Blue Knights had agreed to pay Ticketus back £10m of its £27m over nine years. It is believed the Singapore consortium has agreed to pay the firm back £14m over a shorter period.
David Whitehouse, joint administrator, said: "It is disappointing the Blue Knights are withdrawing at this stage, particularly in the view of the fact that last week it was made clear to them and Ticketus that their indicative bid placed them in a strong position.
"We were therefore surprised that their offer to pay an exclusivity fee was withdrawn."
He added: "Ticketus has also been in parallel discussion with one of the other bidders over the last few weeks and it remains to be seen whether these discussions will be taken forward."