The businessman, who is leading a group of investors attempting to force out chief executive Craig Mather, financial director Brian Stockbridge and non-executive director Bryan Smart, made his comments after the club said this week it could work with one of its proposed directors, accountancy executive Frank Blin.
Mr McColl said: "We would encourage the board to make the changes that we believe are being demanded by the majority of stakeholders in the club."
The two sides reached agreement yesterday on proposals to roll an EGM into the club's annual general meeting (AGM) to save money. The shareholders group had previously wanted separate meetings, which the club said would cost £150,000. The joint meeting is now likely to go ahead in October with the top items on the agenda expected to be the proposed boardroom shake-up.
On July 31, those backing change, said if the directors did not convene within 21 days, they would organise the meeting themselves and bill the club.
Mr Blin is a former executive chairman of PriceWaterhouseCoopers Scotland.
Once the AGM/EGM date has been set, both the board and the requisitioners will start to lobby undecided shareholders for their votes
A Rangers spokesman said: "The chief executive has secured commitment from the requisitioners that they accept Mr Mather's stance and are now willing to roll the two meetings into one session." It added that the original plan for two back-to-back meetings would have been a "waste" of club money.
Meanwhile, it is understood former chief executive Charles Green has begun the process of trying to find buyers for his shares.