Woods claimed his 14th major at the 2008 US Open in a dramatic 19-hole play-off with Rocco Mediate, but has not won one since after seeing his career set back by the sex scandal which led to the breakdown of his marriage.
And Norman, speaking on the eve of the Australian PGA Championship at Coolum, would like to see McIlroy - who has two majors to his name - be the man to surpass Nicklaus instead.
"I don't think so, no," Norman said when asked if Woods was capable of winning the five majors he requires to pass Nicklaus. "Every year that passes by that he hasn't won a major it just gets that much harder to win a major.
"I don't care how many you have won, it just becomes more and more difficult He might win one or two more but I don't think he will win the four or five more that he needs to win to break the record."
McIlroy won the US Open in 2011 and this year's US PGA Championship and Norman says the sky is the limit for the talented 23-year-old.
"I think if anybody can break Nicklaus' record I think he could, because he is young, he is ahead of the game, he is ahead of the curve on a lot of things and he has a very balanced life across the board," Norman said.
"So I will keep my fingers crossed for him because I would love to see that happen. Somebody will do it one day and it could be Rory.
"I am a big fan of Rory's, he can be as big as he wants to be."
Norman was bullish about his chances at this week's PGA Championship but conceded golf is low down on his list of priorities these days.
Asked his goal for the week, Norman quipped, 'to do a Peter Senior', referring to the 53-year-old's victory at last week's Australian Open.