American businessman Bill Miller has unveiled plans for an £11.2million bid which would create what he described as an "incubator" company while Duff and Phelps aim to take the club out of administration through a Company Voluntary Arrangement.
Paul Clark, joint administrator, said: "We would ask the fans to remain patient for a few more days. Discussions will continue over the weekend and we will have an update as soon as there are notable developments."
The towing tycoon left the door open for rivals by suspending his bid until Monday and Paul Murray's Blue Knights consortium have held further discussions with administrators and potential backers Ticketus.
Miller is technically the only bidder still in the running after Bill Ng's Singapore consortium announced their withdrawal, while a new offer from Sale Sharks owner Brian Kennedy was rejected this week.
The Blue Knights took a step back from the bidding process on Monday, although they have since indicated they could return to the table.
Clark said: "At the end of a frustrating week we'd like to provide an update to the fans regarding the bidding process. It should be reiterated, however, that no unconditional bid has been tabled by any party.
"There have been a number of complicating factors in recent weeks, not least the cloud of possible further SPL sanctions against the club and the withdrawal of one of the parties last week when it emerged they had no formal agreements in place with their partners.
"This, combined with uncertainty regarding the role of Ticketus in any future ownership, has led to delays that we and all Rangers supporters would prefer not to have occurred.
"Let me be clear - we could not have moved more quickly during the past week as there was not a bid capable of acceptance. Despite suggestions to the contrary, it is not a case of the administrators refusing to nail down their choice - we can only accept a bid that is unequivocal."