Rangers' administrators have granted Bill Miller preferred bidder status and hope the club will be in his hands by the end of the season.
The America-based businessman aims to form an "incubator" company that would see the assets of Rangers transferred to a new company.
Miller's initial bid was dependent on the Scottish football authorities not imposing further sanctions on the club.
But Duff & Phelps now describe the offer as "unconditional".
The Scottish Football Association and Scottish Premier League both say they intend to hold further talks with Miller, who made his money from a tow truck business.
Any newco club would need to request permission from the SPL board to acquire Rangers' share in the competition.
The "incubator" idea would leave an "old company" saddled with the club's debts and aiming to deal with its creditors via a Creditors Voluntary Arrangement [CVA].
Administrator Paul Clark explained that the two entities would later reunite, saying he thought it was an "entirely workable strategy".
Clark also revealed that Miller's bid was "substantially greater" than the rival offer from the Blue Knights consortium led by former Rangers director Paul Murray and backed by Sale Sharks owner Brian Kennedy.
He added that it would provide "a stable platform" for the club and provide the best return for creditors.
Clark stressed that the bid "avoids the need for liquidation" but did not address what would happen in the event of a failure to agree a CVA.
Rangers are facing a 12 - month transfer embargo pending an appeal against the SFA's decision.
UEFA also insist clubs are members of national associations for three years before they are allowed into European competition.
Sections of the Rangers support have voiced opposition to Miller's proposed takeover.
However,following Wednesday's 5 - 0win over Dundee United, manager Ally McCoist said: "I think everybody has got to be given a chance, whether it's Bill Miller or whoever it may be.