The news came on the day the club's public relations chief James Traynor quit.
The South African-based businessman admitted defeat yesterday in his attempts to reach a deal with Rangers International Football Club shareholders, making an acrimonious annual general meeting almost inevitable.
The shareholder group, including Mr Murray, which is campaigning for change in the boardroom, released a statement demanding the individuals behind Blue Pitch Holdings and Margarita Holdings, who hold a stake in the club, are revealed.
Mr King will not give up on attempts to try to address the club's funding shortfall and lack of strong corporate governance, but he has temporarily withdrawn from the situation.
Mr King said that administration for the newco club is "not an imminent threat", but he does believe it "is a distinct possibility if the AGM results in a continuing lack of continuity on one side or the other".
He praised the approach of current director Sandy Easdale and Mr Murray, but said "certain influential share- holders are unwilling to compromise at this time".
The shareholders nominating Mr Murray, Malcolm Murray, Scott Murdoch and Alex Wilson to the board questioned the identity of the investors behind Blue Pitch Holdings and Margarita Holdings. Their stakes in the club are represented by Mr Easdale, along with shares belonging to Charles Green, the former chief executive, who has agreed to sell his stake to Mr Easdale when his lock-in period ends next month.
The group said in a statement: "Having now reviewed the information supplied to us by the club, we are unable to identify who is really behind these two companies. We are considering all options to ensure that there is full disclosure."
Meanwhile, former Daily Record sports editor James Traynor has left the club less than a year after his appointment as director of communications. His departure is reportedly part of a series of cost-cutting measures.