In a statement on Tuesday night, they revealed they would be prepared to welcome Frank Blin, the former executive chairman of PricewaterhouseCoopers Scotland, on to the board.
But no mention was made of the man who fronted the Blue Knights, the consortium that failed to take over the troubled Glasgow institution, a year ago.
It remains to be seen if the group of shareholders who have requisitioned an EGM accept this compromise.
But I personally would like to see Paul, and others like him, back involved at the highest level at Rangers.
For Paul has, and always has had, the best interests of Rangers at heart - and I want people who genuinely love the club involved.
I know Paul personally. He is a true fan who used to attend every game whether it was at home, away or in Europe. Whenever the club played, wherever they played, he was there.
He could easily have moved on after the Blue Knights failed to be named as preferred bidders by administrators Duff and Phelps. He could have retreated into the shadows and let the successful party get on with it.
But he is clearly very concerned about his club. He wants to see Rangers in what he considers to be the right hands.
As well as being a fan, he is a shrewd businessman. He can see that all is not well and he believes the right people are not running things.
He has enlisted the support of Jim McColl, another hugely successful Scottish businessman, shareholder and supporter.
Some people say Paul should not be brought back because of his involvement with the board previously.
But when he was there before there was only one man running the club and making the decisions - Sir David Murray.
He owned the majority of the shares and decided what happened.
And Paul acted when Sir David was on the verge of selling his stake in the club to Craig Whyte.
He signed a letter along with every one of his fellow board members urging the then owner not to sell the club to Whyte.
For whatever reason, Sir David went over their heads and did it anyway.
I think the vast majority of Rangers supporters are behind the moves being made by this influential group of shareholders for boardroom change.
Ally McCoist is starting to get things right on the park and the fans are delighted with that - but they also believe that the club has to be run properly.
I would imagine the next few weeks will see the EGM being held and the boardroom changes being pushed through. If that is, in fact, the case, then so be it.
The bottom line is that the right people have to be involved in the running of the club.
Dave King, Paul Murray and McColl have no desire to run the club themselves, to take control of the club for personal profit.
No, they just want to see the right people in there running the club behind the scenes.
The club has lost a lot of money. All of the £22million raised in the share offering last year has gone.
I am not saying everybody on the board should go. That would be wrong. There are people there who genuinely care about the club and want it to do well.
At the moment, I think there are two or three members of the board who are like that. But not all of them are.
That situation rightly worries supporters. They were angry when Walter Smith stood down as chairman. When he was there they knew the club was in safe hands.
The board needs help. They need business people with Rangers at heart to go in there and help to run the club.
Charles Green has now gone. Why he was ever brought back in a consultancy role I will never know.
But he was responsible for a lot of upheaval. In the end, they had no other choice but to listen to the will of the fans and remove him.
The supporters are the ones who have kept the club going for the last two years. They have to be heard.