King, who invested heavily in the Scottish giants during Sir David Murray's reign and reportedly lost £20m when they went into administration in 2012, could become the club's new chairman in the coming weeks.
"I confirm that I held talks with Rangers chief executive Craig Mather and finance director Brian Stockbridge in South Africa," the tycoon said in a statement. "The discussions were, to my mind, very positive and it was agreed that subject to the normal regulatory approval I would put my name forward to join the board and to serve as chairman.
"Such an appointment is of course subject to the approval of the existing board members and ultimately the shareholders of the company.
"There are also mandatory regulatory requirements that must be complied with and take time. I have already submitted all the necessary documentation."
Rangers are currently playing in the Scottish League One.