A group of disgruntled investors led by billionaire businessman Jim McColl wants to see the former IBM vice-president returned to the Ibrox boardroom, possibly as chairman.
They have also proposed appointing former Blue Knight Paul Murray, Sandy Easdale - the brother of current non-executive director James - and accountancy expert Frank Blin as directors.
McColl, chairman of Clyde Blowers Capital, and his group had called for an extraordinary general meeting (EGM) in a bid to have chief executive Craig Mather, finance director Brian Stockbridge and Bryan Smart removed from the board, but have now signalled they are ready to withdraw that request so long as their new motion is passed.
A statement given to the Stock Exchange said: "Further to the announcement on September 2, the company confirms that the board's discussions have been continuing with representatives of the group who requisitioned a general meeting.
"Following recent press speculation, the company can confirm that the requisitioners have put forward a proposal to withdraw the requisition based on their request for the appointment of four additional non-executive directors, being John McClelland, a former chairman of Rangers Football Club, Sandy Easdale, an existing shareholder of the company, Paul Murray, a former director of Rangers Football Club and Frank Blin, formally of PricewaterhouseCoopers.
"As part of the proposal, the requisitioners have also confirmed that, subject to the above, they are not seeking to remove any of the current directors."
The call for an EGM came in the wake of an increasingly bitter battle for control of the Rangers boardroom.
The two sides had been close to agreeing a deal that would have seen the EGM motion folded into the business of the club's annual general meeting, due to be held some time in October, saving the club around £80,000.
But today's development could see the entire matter put to bed for good.
However, the current board say they are now seeking assurances that McColl's group will give them their full backing.
Their statement added: "The company confirms that discussions are continuing with the requisitioners with regard to reaching an agreement for the withdrawal of the requisition.
"The board considers that any decision on any proposal for the withdrawal of the Requisition would be subject to the provision by the requisitioners of a vote of confidence and continued support for the current Directors and to all necessary regulatory approvals."
Ex-manager Walter Smith stepped down as chairman last month after controversial former chief exec Charles Green made a short-lived return to Ibrox as a £1,000-a-month consultant, sparking yet another round of infighting amongst the club's directors and investors.