Rangers administrators Duff and Phelps say talks with two interested parties are "very advanced" as they hit back at the Blue Knights.
On Friday, the Blue Knights withdrew their offer for the club after claiming time had run out for them to effect a Company Voluntary Arrangement.
David Whitehouse, joint administrator, said in a statement on Friday night: "The most important information today for Rangers supporters is that discussions with two bidding parties are at a very advanced stage and we hope to reach agreement with one at the earliest opportunity."
One of the groups involved in discussions is reported to have links with former Sheffield United chief executive Charles Green.
Brian Kennedy, who has latterly spearheaded the Blue Knights bid along with former Rangers director Paul Murray, warned on Friday that Duff and Phelps would have "blood on their hands" if the club failed to survive after their ultimatum passed without action.
Kennedy - who had secured a deal to acquire Craig Whyte's shares - valued their bid at £11million, including £5.5million up front, conditional on a CVA being agreed by creditors.
The Sale Sharks owner added that another £2million could be put into the CVA pot dependent on European success while they would pay off the £3.5million owed to football clubs. Kennedy added: "We inherited £3.5million of debtors."
Kennedy and Murray also accused Duff and Phelps of "spin" and misrepresenting their bid.
Whitehouse responded: "It is most unusual for us to comment publicly on individual bids but due to the allegations made by Mr Kennedy and Mr Murray today with the regard to our conduct as administrators we feel compelled to reveal important facts in relation to the various Blue Knights attempts to buy the club.
"For the avoidance of doubt some of the comments made at today's press conference were grossly misleading.
"First I would state unequivocally that every opportunity was afforded to these parties.
"The fundamental reason we could not proceed with the Blue Knights/Ticketus combination was that we were advised there was not agreement within the consortium in relation to the funding of their bid.
"Throughout the process Mr Kennedy told us repeatedly he would be the 'last man standing'."
Whitehouse added: "As Mr Kennedy today made a virtue of explaining publicly details of his bid we are in a position to comment on those remarks.
"Of the £5.5million cash on 'day one' figure Mr Kennedy quoted, £3.5million of that would be provided by us in any case from the club's debtors.
"The bid structure also factors in performance in Europe, and reaching the later stages of the UEFA Champions League which cannot be achieved next season for example."
The Blue Knights, without Kennedy, were previously offered preferred bidder status but could not pay the £500,000 exclusivity fee as their partnership with investment firm Ticketus disintegrated.
The new partnership was later beaten by American Bill Miller, who subsequently withdrew his offer.
Whitehouse said: "We find it extraordinary and very disappointing that Mr Kennedy in particular should assert that the amount being offered is irrelevant.
"Time and again he and others have been afforded the opportunity to become the best bid in play and it has not happened.
"We have a statutory duty to accept the best bid that is deliverable.
"The bid should also be commercially better than the liquidation of the business.
"Mr Miller's bid was deliverable but he chose not to proceed. We firmly believe the best interests of the club would be served by all involved in the process respecting the bidding process."
Kennedy later responded by publishing a letter from his lawyer to Whitehouse.
The letter addresses the value of the bid, pointing out that European income is based on the second and third seasons, that most of the £3.5million from debtors will be needed to fund trading losses in the next few weeks, and that the Knights had agreed to fund "huge" trading losses after June 1, when players' wage cuts finish.
The lawyer, David Hinchcliffe, goes on to stress that the Knights' offer was the only one on the table.
"You seem to be continually comparing the quantum of my client's bid against bids such as the Miller bid which are not real," Hinchcliffe wrote.
"As you know, I have vast experience of people making bids for insolvent football clubs.
"I cannot see how any of these new parties can be making real bids when they have done no real due diligence.
"Proof of funds may have been provided but it does not make sense to me why investors would invest in Rangers without full due diligence by them and I would strongly recommend that full due diligence is carried out by you on these parties as there is no time to have another Miller situation.
"Finally, regarding your comment that Brian wanted to be the last man standing. In mine and Brian's view, he is as we don't believe the other bidders will complete.
"If you want to talk to find a way to save this great club, Brian has said his phone will be on this evening otherwise I fear it will be too late."
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what do you think?
Well what Brian Kennedy said on Friday has won me over as was not to sure. But there are now two things i am sure of is that Brian Kennedy and blue knights bid sounds the best and are of the best interests of our club. And that duff and Phelps are trying to ruin our club completely