The engineering tycoon has admitted he has no plans to buy the League One club despite former chief executive Mr Green's ultimatum.
Mr Green, who returned as a consultant last week, was back in the Ibrox directors' box last night for the club's friendly match against Newcastle United, which ended in a 1-1 draw.
Mr McColl and former director Paul Murray have mounted a bid to oust the club's new chief executive Craig Mather and two others by forcing an Extraordinary General Meeting (EGM).
Mr Green urged Mr McColl to stay away unless he and his associates come up with the money to buy his consortium's stake.
The Yorkshireman has offered Mr McColl 20 million shares in the club at around 70p each, the same price as fans and other early investors paid, and in return said he and other key figures will walk away from the club.
Rangers shares are currently valued at around 41p.
In an exclusive interview with The Herald, Mr McColl said he had no interest in sitting on the board or increasing his small shareholding, but had been motivated to force changes given disenchantment among a section of investors and fans with the current set-up.
Mr McColl said, as a club supporter and small shareholder, he could not sit by knowing that disenchanted investors could ditch their shares and put Rangers' future power to attract capital at risk.
Mr Green yesterday criticised Mr McColl's attempts to call an EGM and parachute Mr Murray and Frank Blin, a former head of PricewaterhouseCoopers in Scotland, onto the board.
Brian Stockbridge, the finance director, and Bryan Smart, the non-executive director, would also go in the coup.
Mr Green said that Mr McColl's earlier discussions with various consortiums to buy a major stake in Rangers had led to nothing, claiming that the latest attempt to overhaul the boardroom was an exercise in vanity.
He said: "What I am saying to Jim McColl is 'look, you are the world's richest Scotsman, you are a billionaire. You have got until Friday to put £14m into stockbroker Daniel Stewart's client account, and me and my consortium will sell you 20 million shares at the same price that all the Rangers fans bought in the IPO and you will have 28% of this club.'
"Then I know you and your consortium are serious about what you want to do, and if you are not going to do it by Friday just shut up and let the club move on."
Mr Green has returned to Glasgow from his home in France claiming he needs to inject "sense" into the boardroom following the sudden departure of chairman Walter Smith on Monday.
If there is no deal by close of business on Friday, Mr Green said his priority would be to defend the club against the EGM and to build a stable, experienced board.
He claimed to have no interest in replacing Smith, who left just three days after Mr Green announced he was heading back to Ibrox, but said he would sit on the board if necessary to achieve stability.
In an interview with The Herald at McGill's bus depot near Glasgow Airport, owned by Rangers shareholder James Easdale and his brother Sandy, Mr Green said: "My concern is that we're going to see a repeat of what we have seen over the past 18 months, where the Blue Knights were going to buy it from Duff and Phelps and did nothing.
"After my consortium acquired the club they came along and were going to buy us out and Jim McColl was in those discussions and nothing happened. Here we are a year later with the same members. I know I am not liked by Rangers fans but even those who don't like Charles Green don't want Paul Murray."
Smith has attacked the board as being dysfunctional and lacking integrity.
Mr Green denied the board had been dysfunctional when he was at the helm of the club, claiming he was like a Gengis Khan figure and that democracies didn't work around board tables of football clubs.
He said: "Rangers needs change and I believe I brought a freshness to it. I sensed when I got there it had to move into an new era. Now I want to finish the job I started."
The notice requisitioning an Extraordinary General Meeting allows a further 15 days for the boardroom changes to be made by the club, or for the EGM to then be arranged to allow shareholders to vote on the proposals.
The notice was backed by just under 29% of the shareholders, but reports claim more than 40% have now indicated that they will support it.
Responding to manager Ally McCoist's claim at the weekend that he is devious and an embarrassment, Mr Green said: "I am a devious man and that is the nicest thing Ally has ever said about me."