The pair will meet with fans' representatives from the Rangers Supporters Trust, Rangers Supporters Assembly and Rangers Supporters Association.
Former Blue Knight Mr Murray and billionaire Clyde Blowers chairman Mr McColl have been embroiled in battling boardroom bosses at the club since August.
In a statement, a Trust 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 publish them and any answers provided on the members area of the website."
The meeting comes a week after chief executive Craig Mather and director Bryan Smart resigned from their posts, leaving just Brian Stockbridge and James Easdale on the club's board.
Earlier this month, Mr Murray won an interim interdict banning the AGM from taking place today.
The former oldco director, who led the unsuccessful Blue Knights bid to buy Rangers before they went into liquidation, was forced to act after Mather and his fellow directors refused to add a motion calling for four new directors to be appointed at the AGM, including himself.
Rangers must now stage an AGM by December 30 and must give shareholders at least 21 days' notice.
The club say they are working "as a matter of priority" to appoint new directors ahead of the new AGM.
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