Sale Sharks owner Brian Kennedy and the Blue Knights have confirmed they have submitted a "revised bid'' for Rangers with administrators Duff and Phelps.
Kennedy and the Blue Knights consortium - fronted by former Ibrox director Paul Murray - are in the running for a takeover of the stricken club, with American tycoon Bill Miller another bidder.
Administrators confirmed they had received formal offers from both interested parties on Friday.
Kennedy's spokesman said: "Brian Kennedy has asked me to advise you all that a revised bid has been submitted to the administrators.''
The Knights were set to be named preferred bidders two weeks previously but former partners Ticketus would not pay the exclusivity fee.
However, Kennedy was told at the weekend that the offer delivered by himself and the Knights on Friday, reported to be worth £5 million, would not be commercially acceptable to creditors.
Rangers' liabilities are around £60 million but they could face an additional tax bill of up to £75 million in the coming days or weeks when a tribunal outcome is delivered.
The offer is subject to a Company Voluntary Arrangement being accepted and Craig Whyte handing over his 85% shareholding.
Joint-administrator David Whitehouse said Miller's £11.2 million bid, which involves transferring the club's assets to a new company, was acceptable and claimed there could be clarity early this week over whether the American could proceed. He added that Miller could theoretically take control before the end of the season.
However, Miller's bid is dependent on getting assurances that his newco club would not be penalised by the football authorities.
A new club would be banned from Europe for three years and the Scottish Premier League clubs are meeting today to discuss points and financial penalties for such a club, while Rangers have appealed against a £160,000 fine and 12-month transfer embargo from the Scottish Football Association.
Miller has been in talks with the SPL and SFA and Whitehouse urged the Blue Knights to follow suit "very urgently".
Rangers manager Ally McCoist admitted on Sunday that liquidation "looks more of a possibility now than it ever has".