The world number one is at the season-ending DP World Tour Championship in Dubai where he is in pole position to land the European tour’s order of merit title for the fourth time.
But the future of the men’s game remains firmly on McIlroy’s mind.
“Greg needs to go. He needs to exit stage left,” said the 33-year-old.
“He’s made his mark but I think now is the right time to say you’ve got this thing off the ground but no one’s going to talk unless there’s an adult in the room that can actually try to mend fences.”
Calling for Norman to step down is one of the Northern Irishman’s strongest comments in the battle between the established tours and the new LIV circuit.
LIV are locked in separate legal cases against the PGA and DP World Tours. McIlroy, who has previously called for both sides to thrash out a solution, believes that is impossible at the moment.
“There are obviously two lawsuits going on at the minute,” McIlroy said. “There’s the PGA Tour versus LIV and there’s obviously this one that’s coming up with the DP World Tour in February.
“Nothing can happen if those two things are going on.
“Right now it is a bit of a stalemate.”
Last week LIV denied a report in the Daily Telegraph that former world number one Norman would be replaced by Mark King who was in charge of club manufacturer Taylormade before moving to a senior position with fast food outlet Taco Bell.
This followed rumours that Norman would step aside having launched the lucrative tour which has staged eight $25m invitational tournaments this year.
Having lured the likes of Open champion Cameron Smith and other major winners, including Dustin Johnson, Bryson DeChambeau and Brooks Koepka, LIV are planning a 14 event super league next year.
February’s legal hearing will determine whether European players such as Lee Westwood and Ian Poulter will be banned from the DP World Tour.
It should also sort out the thorny issue of Ryder Cup selection, with the biennial competition starting in late September in Rome. As it stands American LIV recruits are likely to be banned from playing.
The Saudi Arabian-funded circuit are promising to make a raft of new signings by the end of this year.
The introduction of the LIV Tour has prompted the PGA Tour to increase prize funds and the American-based circuit will introduce a series of $20m tournaments for the world’s best players next year.
Norman says PGA Tour players including Tiger Woods and McIlroy should be “thankful” for what LIV has brought to the game.
But McIlroy insists 15-time major winner Woods is the figure who deserves most gratitude from the leading players.
“I’ve said this a million times: Tiger is the reason that we are playing for as much as we are playing for,” said the four-time major winner.
“Tiger is the reason that the stature of our game is where it is. The generation of Tiger and the generation coming after Tiger have all benefited from him and his achievements and what he’s done for the game of golf.
“I don’t think Tiger should be thankful to anyone for anything. I think everyone else in the game should be thankful.”
At the moment there seems little sign of a settlement to the dispute that has rocked men’s golf in 2022. But McIlroy believes the emphasis will alter next season.
“I don’t think it will have another year like this one because all of the noise has been about who is jumping ship, who is going where, who is staying, who is going,” he said.
“Very little of the storyline has actually been about the golf. So I think next year, if we can get the storylines to being about the golf and what’s happening on the course, that’s a good thing.”