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The Blue Knights have issued Rangers administrators Duff and Phelps with a stark warning that time has almost run out to save the club after they withdrew their own bid.
Sale Sharks owner Brian Kennedy and former Ibrox director Paul Murray, who has fronted the consortium, had issued a noon ultimatum to Duff and Phelps.
Administrators said on Friday night that discussions with two bidding parties are at "a very advanced stage" after American tycoon Bill Miller withdrew his offer within days of being named preferred bidder.
The Blue Knights' bid - which they valued at £11million - involved exiting administration via a Company Voluntary Arrangement (CVA).
They fear it is now too late for a CVA to be agreed and say a newco option, favoured by Miller, is simply not financially viable.
Kennedy said: "It's too late. This is not some clever brinkmanship. This is our lawyers telling us that if we want them to do a proper CVA, professionally put-together, we need a team of lawyers in Ibrox (on Saturday morning) at 9am, otherwise they cannot deliver a CVA for the start of next season.
"When you have got an institution like this that is at death's door, what is important is deliverability, not just quantum, which is substantial.
"We cannot afford to make another mistake. Duff and Phelps better have a good, credible bid on the table that doesn't fall over."
Murray added: "A CVA is now looking very, very difficult in terms of timescale.
"The newco, which is the easiest option in terms of deliverability, we believe is financially so difficult and has a range of other football issues.
"It didn't surprise us that Bill Miller quickly withdrew from the process. The sums of money involved in a newco structure are very large.
"Unless Duff and Phelps have got a plan that I haven't seen so far, then I think we are in a real crisis.
"Time has now run out. Decisions that are made now are absolutely critical to the future of the club.
"I hope they are making the right choice. They have made other choices in the past that have turned out not to be the right ones for the club.
"I really hope this time they've got it right. If they haven't, the future is pretty bleak. This is absolutely critical now."
The Blue Knights' plan involved former Scottish Rugby Union chief executive Gordon McKie working on the financial and operational side of the club and former Ibrox bosses Walter Smith and Graeme Souness working alongside manager Ally McCoist as part of a football board.
Kennedy, who revealed he had agreed a deal with Craig Whyte to acquire his 85% shareholding, said: "Anybody with a brain in their head can see this as a credible plan, that is fully-funded by credible people with the right motives.
"By virtue of the fact that Duff and Phelps have chosen not to go with us as preferred bidder, they better have somebody good, some good credible consortium, fully-funded, who does not fall away next week and the result being the liquidation of Rangers Football Club."
He added: "Graeme and Walter had agreed to come in on a part-time basis, probably a non-executive basis, with a view to helping Alistair create long-term strategy, going out and finding the best players at the best prices with good prospects for the future.
"For the three of them to be able to do that working collectively, we all thought would have been an absolutely phenomenal team to come together."
Murray said the press conference was called partly to provide clarity over the bidding process after claiming the Blue Knights had been mis-represented by administrators.
He said: "It's important that we explain our position because there has been a lot of mis-information and spin which has been created in this process.
"We have been mis-represented on a number of occasions.
"People are trying to help the club and, let's be clear, the people involved here are all people with Rangers' interests at heart.
"There is no-one doing this to make money. I can assure you, this is not a way to make your fortune.
"I find it perplexing that Duff and Phelps almost try to question why we are doing things and mis-represent us. I find that bizarre."
Kennedy expressed surprise at the emergence of new bidders this week in the wake of Miller's withdrawal, with reports claiming former Sheffield United chief executive Charles Green is involved with one of the groups.
He said: "I think we are all surprised, aren't we? Suddenly these guys pop up from nowhere. Where have they been for the last three months?"
Murray added: "This is the most complex thing I've been involved in in 25 years so, quite frankly, for someone to arrive last week and try to figure all of this stuff out, for me, is bemusing."