The former oldco director was responding to reports on Wednesday morning which claimed the reigning board - led by chairman David Somers - have already secured enough votes to retain their roles ahead of Thursday's annual general meeting.
The reports also suggest Murray, who also sat on the oldco board, and his fellow "requisitioners" Malcolm Murray - the former newco chairman - Alex Wilson and Scott Murdoch would fail in their bid to force themselves into directorships.
But King - who insists he is still "more than keen" to get involved with the running of the club - says hiring Murray would help heal the wounds inflicted by the club's bitter civil war.
The South African-based businessman said: "I would hope that if this does turn out to be true [that the current board have won] they will reach out a little bit and invite Paul Murray onto the board.
"I think it would help them, if their position is secure and they know it to be secure, to at least get Paul on board.
"I can't comment on Malcolm Murray and whether he should be invited on as I have only met him a couple of times and that's the same with the other two gentlemen, who I don't know at all.
"But it would really help the incumbents to get someone of Paul's experience on to the board. He's a good Rangers man and a good businessman. He knows what it's about and is interested in the club for all the right reasons. It makes good business sense
"I think it would send the right signal - almost an olive branch - to the supporters. It would be a very smart thing to do. It would be a very sensible, pragmatic and practical gesture from the board.
"That might help the fans because they would have a high level of confidence in Paul's attitude and experience. They would know he would be there for the right reasons and for the long term."
The requisitioners have the backing of the Light Blues' rank and file, who have reacted angrily to the actions of the current board - which also includes chief executive Graham Wallace, under-fire financial director Brian Stockbridge, James Easdale and Norman Crighton - and even held a red card display during their last home game against Ayr United on December 7.
But Glasgow-born tycoon King believes the current board can win over their critics.
He said: "One of the difficulties that the Rangers fans have had for a couple of years now is that they haven't been anywhere near the top of anyone's considerations about what's been happening at the club.
"They have been dealt with once or twice a year when [the club] needed money from season tickets.
"There's been so much bickering and squabbling, changes in ownership and arguments about who is behind it all and who is not.
"But the one thing we will get after tomorrow is some certainty. The shareholders are the shareholders and we can't wish them away. They will vote in accordance with their own interests.
"But the important things after this is how do we move forward? At least we will know who is captaining the ship but then it is about working out how to get the funding it so desperately needs.
"It's very important for whoever is running the club after tomorrow that they can outline a proper financial plan, because with next year's season tickets still to be bought, that would at least let the fans know the club is being dealt with in a manner that satisfies all stakeholders."
King ploughed £20million into Rangers during Sir David Murray's reign as chairman but lost his investment when Craig Whyte led the club into liquidation.
However, he flew into Glasgow last month to hold talks with both sides of the boardroom divide - and was even offered the chairmanship of the club's football board by the reigning PLC directors.
Now King - who has settled a long-running dispute with the South African tax authorities - says he is ready to commit himself again once the AGM votes are resolved.
"When I was over a month or so ago, no-one really knew - neither myself or the people I spoke to - with any certainty what the position would be post-AGM," he explained.
"But in a fairly short period of time I will be in a position of knowing who exactly will be at the helm going forward. After that we will be able to have those conversations.
"But am I still keen to get involved? Absolutely, absolutely. More than keen.
"The actual role would depend [on future discussions] but certainly to help with attracting investment. A lot depends on the shape of the club after tomorrow. If there is still a chairman there then there's still a chairman and that's fine. We will see how it goes."