Manager Ally McCoist believes Rangers are heading into a "massive" period of 48 to 72 hours as the club edges closer to finding a buyer.
Former Ibrox director Paul Murray's Blue Knights and Sale Sharks owner Brian Kennedy have been in talks over rejoining the race for the stricken Glasgow giants.
The Blue Knights took a step back from the process on Monday before indicating they could return to the table following talks with administrators and potential backers Ticketus, while Kennedy saw a second bid rejected by Duff and Phelps this week.
American businessman Bill Miller is the other interested party, who said he would suspend his bid until Monday to allow other bidders to "put up or shut up."
McCoist - speaking after the 3-0 win over Hearts in the Clydesdale Bank Premier League - said: "I've got to be positive.
"There is plenty to worry about if you wanted to but there is no way we can do that. We have to be positive and optimistic.
"I spoke to Paul again last night and I spoke to Brian Kennedy yesterday and when you have got guys like that, who do have the club's best interests at heart, then we have definitely got a chance.
"We are all aware of the pitfalls that could be around the corner but it won't help with me showing negativity.
"It's a massive 48-72 hours for us. It really is massive for the football club. I'm just hopeful we can get through it."
Asked if he was hopeful there would be offers on the table by Monday, the Rangers boss added: "I'm really hopeful that would be the case. These next 48-72 hours are absolutely vital for the club.
"I haven't spoken to anybody from Duff and Phelps today but I will speak to them tonight or tomorrow for an update. I remain very hopeful, as one has to."
Miller unveiled plans for an £11.2million bid for Rangers on Friday which would create what he described as an "incubator" company while Duff and Phelps aim to take the club out of administration via a CVA.
However, his offer includes the condition that the Scottish Premier League do not impose sanctions on the club next season. The SPL meet on April 30 to discuss financial fair play proposals relating to clubs in administration or going into liquidation.
On Miller's plans, McCoist said: "To be 100% honest, I haven't really studied it because it was only released about 4pm yesterday and the game has been of paramount importance to my staff and myself.
"I have looked at it but I don't know enough about the legalities of it.
"There are certainly no guarantees. I don't think we are in a position to ask anybody for guarantees to be quite honest with you.
"All we would hope for is that we get some fairness. I wouldn't say some leniency but some fairness and realism from the powers that be.
"That's all we can ask for because we are in the wrong and we have to accept that. We just hope for a positive outcome."