King, formerly the chief executive officer of golf equipment manufacturer TaylorMade and the president of shoe giant Adidas, is currently the CEO of US fast-food chain Taco Bell.
He is an avid golfer, The Telegraph says, who was present at several LIV events in its inaugural season this year and has met with Yasir Al-Rumayyan, the head of the Saudi Public Investment Fund that is bankrolling the circuit.
King, 60, recently told the Fire Pit Collective he believes "in five years LIV Golf will be another tour among existing tours and that everybody will learn to get along".
Norman could be "moved upstairs" in the LIV organisation if King comes aboard, The Telegraph suggests.
Norman was the face of LIV Golf as it launched, helping the breakaway tour attract stars including Phil Mickelson, Dustin Johnson, Bryson DeChambeau, Patrick Reed, Bubba Watson, Sergio Garcia, Lee Westwood and fellow Australian Cameron Smith.
Players received up front payments as high as a reported $US125 million ($A190 million) for Johnson to jump ship to the LIV franchise.
One player Norman notably failed to sign was Tiger Woods, even though Norman told Fox News he offered the 15-time major winner between $US700 million and $US800 million.
Norman was the world's top-ranked player during a career that saw him win the Open in 1986 and 1993 and finish second eight times in major tournaments.
