Former Gers director Murray is a member of a group of disgruntled shareholders trying to force through changes at boardroom level.
However, he has welcomed the prospect of King, who has settled his outstanding tax issues in South Africa, getting involved.
And he stressed he would be able to work alongside the Castlemilk-raised multi-millionaire if he decides to plough more money into the club.
Murray said: "I think he would be a fantastic guy to have in the club again. I don't know what he thinks. I last spoke to him about six weeks ago or so. But he has obviously got the same concerns as we have got about the club.
"I think he said publicly that he will invest in the club, but he just won't give any money to the existing shareholders.
"If the club does need money, which I think it will do in the next 12 months, Dave has said he would be happy to lead that investment. I'd be happy to have him alongside me. But, remember, I don't have to be involved here.
"If Dave King arrived tomorrow, bought the club and said 'Paul, I don't want you' I would be absolutely delighted. "I would go then. I would say: 'Fantastic. The club is safe'. I would go and watch the games, no problem."
Murray also dismissed claims he could not serve as a Rangers director due to his previous involvement with the oldco board.
He said: "I have no doubt I am a fit and proper person to join the Rangers board. I would pass the SFA rules."