Norman, who will soon stand down as LIV Golf's chief executive, says the decorated duo should acknowledge how the Saudi-funded circuit has helped them.
US PGA Tour stalwarts Woods and McIlroy have both been outspoken critics of LIV Golf and Norman, saying the Australian should exit his role to heal the rift between the tours.
In response to LIV, which this year will stage its fourth season, the PGA Tour boosted prize money with $20 million signature events and pumped more money into the Player Impact Program (PIP).
"I would love them to recognise the fact that, like Tiger with his PIP money, that only came because of LIV, right?" Norman told Australian Golf Digest.
"So Tiger benefited from that. Rory has definitely benefited from that.
"I would love to sit down and talk to them about it, no question about it, because I'm not a judgmental person and you only learn the facts and truth when you hear the other side of it.
"But, yes, would I like to sit down with them? Sure, absolutely.
"And you know what? I'd win the debate."
Norman has been a fan favourite at LIV Golf's Adelaide tournament. (Michael Errey/AAP PHOTOS)
Woods and McIlroy have formed the TMRW Golf League (TGL), a made-for-television format where players compete on golf simulators.
"No, I haven't watched a bit of it because there's a couple of players who've been very vocal against me," Norman said.
"So I'm not going to say anything positive or negative about it.
"All I can say is: the more golf gets exposure in different ways, the better off it is.
"Simulator golf is simulator golf ... innovation is a wonderful thing, I'm not going to belittle that.
"I wish them all the very best and success because it's the market, right? They're going to be pulling people in to the game of golf."
Norman's tenure as LIV's chief executive ends on August 31 this year with long-time sports and entertainment executive Scott O'Neil to replace him.
"Once my official tenure at LIV is up ... I will stay involved with LIV in some way, shape or form," he said.
"I'm going to stay on the board so there will be that part of my life but it won't be as consuming as what it was before.
"When I look back on my past three-and-a-half years, from my past 20 years, oh my gosh, I really have changed the game of golf more than what people realise."
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