McIlroy welcome on LIV Golf but no offer made for PGA Tour star
A report in Britain last week said McIlroy - a long-time critic of the upstart Saudi circuit - was poised to switch to LIV in a staggering deal worth $850 million (£682m).
But the four-time major winner from Northern Ireland swiftly debunked the rumours in an interview with NBC's Golf Central.
"LIV never put an offer to him," Norman said when asked by AFP on the sidelines of LIV's latest stop in Adelaide.
"This is just typical white noise that gets out there in the industry."
LIV has signed a slew of golf's elite since its formation, with Spanish star Jon Rahm the last big name to make the switch last December in a move reported to be worth around $500 million (£401m).
McIlroy has been increasingly conciliatory towards LIV professionals in recent months amid negotiations with the PGA Tour over a merger, but insisted to NBC he planned to remain on the PGA Tour "for the rest of my career."
Norman said he would always be welcome should he change his mind.
"If Rory was willing to sit down with us and have a conversation with us, would we be happy to sit down with him - 100 percent," he said.
"No different to any other player who would be interested in coming over to play with us."
Norman revealed he recently sat down with another "top, top PGA player" to lay out the facts of what LIV represented and what it could deliver on a global basis.
'Strong' Masters fan support
"I mean I've sat down with one top, top PGA player in his house with another member of my team and walked him through the whole process," he said.
"And he was so impressed and he said, 'that's not what we're told in the locker room', and that this was really impressive.
"He made the decision and he called me up two days later and said 'I'm deciding to stay where I'm at'.
"I said, 'happy days, you made the decision on facts. The door is always open if you want to come back and have a conversation'."
Norman was at the Augusta Masters earlier this month, primarily to "support the (LIV) boys".
After being snubbed from the official guest list last year, he bought his ticket this time and spent three days walking a golf course with the public for the first time in his life.
He admitted to being nervous about the reception he might get, but said the support from fans for LIV Golf's mission was "very, very strong".
"To see it and to hear the comments they made about what's happening to the game of golf and what LIV has brought to the game of golf, it was very, very strong for me," he said.
"It was a very powerful three days."