Billionaire Clyde Blowers chairman McColl and former Blue Knight Murray have been battling boardroom bosses at the club since August.
The club announced £14.4million losses for the 13-month period to the end of June amid allegations of failings in corporate governance.
Murray now hopes to win a seat at the board table when the club finally holds its annual general meeting before the end of the year following his victory at the Court of Session last week which ordered the postponement of Thursday's planned meeting.
Now the ex-oldco director and ally McColl will meet with bosses from the Rangers Supporters Trust, Rangers Supporters Assembly and Rangers Supporters Association to spell out what they have planned.
In a statement released to its members by the RST, a spokesman said: "The RST are pleased to confirm that Paul Murray and Jim McColl have responded to our latest request, and has agreed to a meeting with us, and our sister organisations, the Rangers Supporters Assembly and Rangers Supporters Association.
"We will endeavour to ask as many of your questions as we can, and will, of course, publish them and any answers provided on the members area of the website."
In August, the club told the Stock Exchange that McColl and Murray were behind a bid to have an extraordinary general meeting called to discuss removing then chief executive Craig Mather, director Bryan Smart and finance director Brian Stockbridge from the board, replacing them with Murray and Frank Blin.
A deal was struck to stave off the need for an EGM but Mather later blocked a fresh bid by Murray to have motions calling for himself, Malcolm Murray, Scott Murdoch and Alex Wilson named as directors from being included in the list of business discussed at the AGM.
That sparked Murray's legal bid, which was successful as he won an interim interdict banning the shareholder meeting from taking place on October 24.
In a fresh twist last Wednesday, Mather and Smart then resigned their posts, leaving just Stockbridge and James Easdale in charge of the club's board.
The club say they are working "as a matter of priority" to appoint new directors ahead of the new AGM, which must take place before December 31.