Alan MacKenzie, a 66-year-old from Glasgow who now lives in Australia, was set to pump £1million into the Save Rangers fund when they were in administration back in 2012.
But he invested half of that at a share offering that raised £22million later that year.
Now, though, he has urged South Africa-based businessman King to buy out the shares bought by his fellow fans.
In an open letter to King and other Rangers supporters, he writes: "He (King) should consider doing the honourable thing by those fans who put their hard-earned cash and savings into the club.
"Given his resources he should buy out shares and take the reins he thinks he should control in order to recoup monies previously lost."
According to MacKenzie, he was told by King: "Why should any new investor bail out existing investors because they overpaid for their shares?
"The club needs money not complaining shareholders."