Rangers administrator Paul Clark has told the Blue Knights they have until Monday to make a decisive move to buy the club - or they will proceed with Bill Miller's "newco" proposal.
On Friday American businessman Miller 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 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 held further discussions with administrators and potential backers Ticketus on Friday.
And 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 told Clyde 1 Super Scoreboard on Friday night: "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.
But Clark 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."
"We can however say that if these issues could be addressed the structure of the bid has potential."
Talks are believed to be ongoing with the football authorities and Miller told his rivals to "put up or shut up".
"The time for talk is over," he added. "The club is in serious jeopardy of dying. 'Real' liquidation is looming."
Ng earlier criticised both Duff and Phelps and Ticketus, who are owed £27million of season tickets over three years, for changing their demands as he withdrew.
The chairman of Singapore top flight club Hougang United also said there was "no guarantee" his group would acquire Craig Whyte's 85% shareholding if they agreed a price.
Duff and Phelps defended their approach saying there had been no bid capable of acceptance so far and Clark insisted Whyte would not be an impediment, although he denied his firm had ever labelled the owner an "irrelevance".
"I have always said that those shares will either be given up in some manner or else there will be a mechanism to acquire those shares," Clark said.
"I remain unerring in that view."