During an interview with Paul Kimmage of the Independent (h/t Doug Ferguson of the Associated Press), McIlroy said Norman's previous comments suggested he was "brainwashed by the PGA Tour" is when the beef began.
That it came after Norman sent him an encouraging message after he lost a four-shot lead during the final round of the 2011 Masters made it that much worse in his eyes.
"We've had this really nice back-and-forth, and he says that about me," McIlroy said.
Ferguson noted that McIlroy and Tiger Woods have both said the only way for the PGA Tour and LIV Golf to reach an agreement and perhaps come together is if Norman is no longer in his position.
"I think Greg needs to go. I think he just needs to exit stage left," McIlroy said while also adding there needs to be "an adult in the room."