The South Africa-based businessman confirmed last week that he is willing to work with the Ibrox board after they saw off a coup for power at Thursday's AGM from Paul Murray and his three fellow-requisitioners.
Former director King ploughed £20million into his boyhood heroes during Sir David Murray's reign at the club and boss McCoist knows fans would laud his return if he can strike a deal with the Light Blues hierarchy.
He said: "I would welcome any sort of investment. Dave King has already put his own money into the club. He has certainly proven and been shown to be a Rangers supporter that wants the best for the club. I would be very optimistic that (chief executive) Graham (Wallace) would talk to him.
"I can't speak for Graham when he is not here but I know he is actively looking to pursue new investment.
"If Dave was wanting to come in and do that, I would give him Graham's phone number! From a fans' point of view, it is somebody they know.
"It is a while since he has been involved with Rangers. But I think the vast majority, if not all the fans, look at Dave and see somebody who is a Rangers supporter and is willing to invest.
"From their point of view, I imagine it would be a no-brainer (for him) to talk to the current board. I haven't spoken to Dave for some time but I did read the reports that he was looking to get back in. Fresh investment would obviously be a good thing."
While the return of King would be greeted with huge optimism by Rangers fans, tension continues to linger between the stands and the boardroom in the wake of a fiery AGM that saw Wallace, chairman David Somers, finance director Brian Stockbridge and directors James Easdale and Norman Crighton win the backing of shareholders.
Supporters threatened to 'disengage' from their club if the board was successful last week and it remains to be seen if the Light Blue legions will once again stump up for season tickets and merchandise as they continue to vent their anger at the Ibrox hierarchy.
McCoist said: "The fans are certainly the most important part of our club and always have been and always will be because we wouldn't be here if we didn't have the 72,000 season tickets over the last two years.
"So they must continue to support the club for the club to survive and improve and progress.
"There's absolutely no way I'm going to sit and tell the fans what to do because they have been absolutely fantastic and what they do and say will have a major bearing on how we move forward and I'm happy with that."