Rangers administrators have issued the Blue Knights with a Monday deadline to make a decisive move to buy the club.
Should Paul Murray's consortium not have made a firm offer by then, the Glasgow club will proceed with a takeover by American businessman Bill Miller.
The towing tycoon plans to make an £11.2m offer and form an incubator company to but Rangers' assets and see them exit administration.
Administrator Paul Clark said: "If there is no better offer, we would be looking to proceed with Mr Miller very early next week.
"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."
Rangers were deducted 20 points when they went into administration in February.
