Mr Murray, who helped lead the Blue Knights, which tried to take over the club when it was in administration last year, Mr McColl, the chairman of engineering group Clyde Blowers, and former Rangers chairman Malcolm Murray met fans' representatives in a meeting that lasted 2½ hours.
It took place at Mr McColl's East Kilbride HQ.
Members of three fans' groups, the Rangers' Supporters Assembly, Association and Trust, called for the talks to hear the Murrays and McColl plans for the club after the resignations of Ibrox chief executive Craig Mather and non-executive director Bryan Smart.
Mr Mather and Mr Smart's departures last week leave just Brian Stockbridge and James Easdale on the club's board.
The Evening Times reported yesterday that supporters said they had been given positive assurances about the club's future if Mr McColl and Paul Murray win their boardroom battle.
The groups said their meeting with the board bidders was "very successful".
They told the fans they were happy to consider working with the supporters if they manage to oust Mr Stockbridge and Mr Easdale.
The two Murrays - as well as allies Alex Wilson and Scott Murdoch - hope to win directorships, when the club finally holds its annual general meeting.
Minutes from Thursday's meeting were sent to the Evening Times and reveal the two Mr Murrays and Mr McColl back fan involvement.
The minutes read: "The intention is firmly to work towards proper fan involvement.
"All three of the hosts confirmed their support for this. The nitty-gritty detail needs to be addressed.
"But a future shareholder structure where financial institutions, high net-worth individuals, and individual fans, and fans' organisations all had significant holdings would be welcomed.
"The group would canvass the support for input before anything was implemented."
Earlier this month, Paul Murray won an interim interdict banning the AGM from taking place.
He acted after Mr Mather and his fellow directors refused to add a motion calling for four new directors to be appointed at the AGM, including himself.
Yesterday, reports linked an approach being made to former SFL chief David Longmuir to take up a senior role.
Rangers are operating without a chairman or a chief executive following the recent resignations of Walter Smith and Mr Mather.
However, Mr McColl and the Murrays say they have a man in mind to take over the running of the club.
The minutes said: "The hosts have detailed views on financial issues, but their main concern is to create a structure at the club led by a quality CEO (chief executive officer).
"They have identified and had discussions with a suitable candidate whom they believe would work with them. They have also targeted a highly credible head of finance.
"Making such high-profile appointments will, they believe, gain further support from the major financial institutions invested in Rangers."
The club announced £14.4million losses for the 13-month period to the end of June but the rebel shareholders say there are still institutional investors in the City ready to plough cash into the club.
The minutes added: "There are a number of prospective investors.
"The institutions have indicated future support if a suitable structure is put in place. A number of individuals are considered prospective investors under the same pre-requisite."
Rangers must stage an AGM by the end of December and must give shareholders at least 21 days' notice.
The club said it was working "as a matter of priority" to appoint new directors ahead of the AGM.