Brian Kennedy and the Blue Knights consortium have submitted a revised offer for Rangers.
Administrators had told the group that their earlier bid did not match the one submitted by American Bill Miller.
Kennedy told BBC Scotland: "We've been in extensive negotiations with the administrator over the weekend in a bid to provide a deliverable offer that is acceptable."
Rangers have been in administration since 14 February.
Having had an offer of his own rejected, Sale Sharks owner Kennedy has joined forces with the Blue Knights' attempts to rival Miller's bid.
American trucking tycoon Miller is seeking assurances from Scotland's football authorities that Rangers will face no further sanctions ahead of next season, with the Ibrox club having already incurred a 10-point Scottish Premier League penalty for going into administration.
Rangers in administration
- Process began on 14 February
- Club deducted 10 SPL points
- Players and management agreed wage cuts to enable season's fixtures to be fulfilled
- Deadline for securing Uefa licence was missed but club have applied to play in Europe next season
- Celtic confirmed as SPL champions on 7 April
- Rangers 11 points clear of third-place Motherwell with four games to play
Both bids are subject to conditions with the Blue Knights seeking a Company Voluntary Agreement (CVA) with creditors, and Miller's offer depending on the outcome of further potential sanctions from the football authorities.
The Knights also want club owner Craig Whyte to hand over his 85% shareholding.
Rangers' administrators have launched an appeal against a £160,000 fine and 12-month transfer embargo imposed on the club by the Scottish Football Association.
SPL clubs met at Hampden on Monday to discuss financial fair play proposals, which could have a significant impact on the Ibrox club, but have
delayed voting on the subject
for at least a week.
The impasse over whether to introduce tough new rules for clubs who are in administration or face the prospect of liquidation would appear to muddy the waters yet further in terms of Rangers finding a buyer.
Rangers supporters marched to the national stadium at the weekend in protest at the SFA sanctions.
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