Rangers administrator Paul Clark has issued the Blue Knights with a deadline of Monday by which to make a decisive move to buy the club, or they will proceed with Bill Miller's "newco" proposal.
American businessman Miller on Friday unveiled plans for an £11.2million offer, explaining that he would form an "incubator" company to buy Rangers' assets and the existing club would exit administration through a Company Voluntary Arrangement at a later date.
Miller, who has confirmed he views Ally McCoist as the club's long-term manager, claimed the plan would preserve Rangers' history, as the two companies would eventually merge.
However, the towing tycoon left the door open for rivals by suspending his bid until Monday and Paul Murray's Blue Knights consortium on Friday held further discussions with administrators and potential backers Ticketus.
There is a huge amount of uncertainty about the feasibility of Miller's bid given he has attached the condition that he receives written guarantees that his new Rangers would not be hit with penalties next season.
But, as Singapore businessman Bill Ng earlier withdrew his bid and Sale Sharks owner Brian Kennedy had a revised verbal offer rejected 24 hours earlier, it appears the Blue Knights are the only potential rival.
Clark said: "If there is no better offer, we would be looking to proceed with Mr Miller very early next week."
The Blue Knights were set to be offered exclusivity seven days ago but could not immediately raise the £500,000 fee and stepped back from the process.
However, Clark on Friday said: "We have been in ongoing contact with the Blue Knights and they tell us they are back in and keen to pursue their interest.
"I have had discussions with Paul Murray and various Blue Knights advisors today and made it clear I would be prepared to continue those discussions over the weekend.
"The door is still open but Monday really is the last day and we really will have to proceed one way or another. It really is a last-chance weekend."
Meanwhile, Steven Whittaker has challenged administrators to resolve Rangers' financial problems after claiming the players have done all they can to ease the pressure on the cash-strapped club.
The first-team squad and coaching staff in March agreed to wage cuts of up to 75 per cent until the end of the season in a bid to avoid widespread redundancies after the Glasgow giants were forced into administration on 14th February.
And, as far as Whittaker is concerned, that timescale should be long enough for Duff and Phelps to find a resolution as they continue the search for a new owner.
He said: "I think we've given them enough of a chance to try to sort it out. Three months is a long time and hopefully we can get it done in that three months.
"We got put in the situation where we took the cuts to give them the opportunity to get things sorted.
"We feel like we have done that and now it's up to them to do their part. We can only sit back and wait. The sooner the better."
Rangers supporters have campaigned against the end of the existence of the club formed in 1872 but Miller said he had no "plans for liquidation" and that there had been a "naive understanding" of the CVA process.
Miller decided a CVA would be too risky and prolonged, claiming major creditor Ticketus would block one, although he has never spoken to the investment firm, and declared he had found a new solution.
In a statement, he said: "If this process continued on for a long period without resolution, the inevitable result would be real liquidation.
"In order to preserve the club's history, records, championships and assets, I will put the heart of the club into an 'incubator' company while Duff and Phelps works to make the sick patient healthy through a CVA process that effectively works to radiate the toxicity of past administrations' sins out of the patient while the healthy heart is preserved and moves forward.
"Once the CVA process has been completed and the patient is on the mend, the administrators will return Rangers Football Club plc to me for a nominal sum.
"The healthy heart and the healthy patient (The Rangers Football Club plc) will then be reunited through merger."
Clark interpreted the situation in more technical language, as the joint-administrator said: "Mr Miller has made it very clear that the actual assets of the club he would be seeking to buy into a newco.
"He has also looked at the situation and very clearly taken on board the fans' concerns and the erroneous reference to liquidation. He would try to get the old company back at some later date."
Clark added: "Certainly it's feasible to deal with a sale of the assets. In terms of dealing with the CVA at a later date that is certainly something that could be achieved.
"I think that we would need to better understand how precisely he wanted to go through that process but that is a later date."