Brian Kennedy could "reconsider his position" over his interest in Rangers after the Blue Knights took a step back from the takeover process on Monday night.
The Sale Sharks owner saw a previous bid rejected for being too low and said at that time he would return to the table if he felt the club's future was in jeopardy.
Kennedy said: "I do not want to distract the time critical process of appointing preferred bidders. However should this fall through with the effect of endangering the existence of RFC, I would reconsider my position."
Former Ibrox director Paul Murray's Blue Knights consortium pulled out on Monday night, leaving a Singapore-based consortium led by Bill Ng set to be named as the preferred bidder.
The Blue Knights were offered the chance to enter into exclusive talks with administrators Duff and Phelps over concluding a deal.
But, during a delay in attempting to raise a £500,000 fee to do so, their financial backers Ticketus, the investment firm whose money financed Craig Whyte's takeover of the club last May, with funding set against revenue from future season ticket sales at Ibrox, agreed a deal with the Singapore group that the Blue Knights claim they cannot match.
In an effort to prevent the Govan club from being liquidated due to further delay, Murray's group have moved aside in the hope that Ng can conclude a deal quickly, although they could re-enter the fray if no agreement is reached.
American businessman Bill Miller is the other party interested in taking control of Rangers.
Speaking earlier this month, Kennedy told Press Association Sport he did not want to go head-to-head with the Blue Knights but is so fearful of Rangers being liquidated, that he will offer the administrators an alternative if they choose another bidder.
He said at the time: "I will not compete against the Blue Knights. But if the Blue Knights bid is rejected, and the bid accepted is going down the route of liquidation, I have left it open to the administrators to approach me to ask for an alternative bid."