McIlroy, the reigning PGA Tour Player of the Year and the No. 1-ranked golfer in the world, won his second major championship in 2012 and emerged as the game's top player.
Meanwhile, Woods rebounded with three victories this year, including a win at Nicklaus' Memorial Tournament -- where he tied the Golden Bear with his 73rd PGA Tour victory.
Woods, though, has been stuck on 14 major titles for four years, slowing his goal of topping Nicklaus' mark of 18.
"When you really don't have a pushing competitor, a force that is pushing you ... his force pushing him has always been my record," Nicklaus said. "And it may get stale during a period of time.
"Maybe somebody else gives you a little kick and gives you a boost. Tiger certainly hasn't lost his talent, certainly hasn't lost his desire. But he's got a few more guys out there now who can finish coming down the stretch than he did a few years ago."
McIlroy, 23, won consecutive tournaments in September at the Deutsche Bank Championship and the BMW Championship to surpass Woods, 36, in victories for the year. He also finished second in the FedEx Cup standings to Brandt Snedeker, with Woods third. McIlroy later won the season-ending European Tour event in Dubai, giving him the money titles on both tours.
Earlier in the year, McIlroy won the Honda Classic, holding off Woods, who shot a final-round 62 to finish second.
"It'll definitely be helpful for Tiger," Nicklaus said. "Tiger probably needs somebody to pop him a few times so he gets a chance to go pop him back. It's kind of good for you to get drummed a couple of times, and all of a sudden he says, 'I'm not getting drummed anymore. I'm going to go drum that guy back.'
"That's sort of what rivalries are all about. They always want to win. The competition is fierce, and that's good."
Nicklaus, 73, is playing with son Gary in the Father/Son Challenge this weekend and will be grouped Saturday with Arnold Palmer and his grandson, Will Wears.
When Woods won the AT&T National in July, he passed Nicklaus on the PGA Tour wins list for No. 74. Only Sam Snead, with 82, has more.
On Thursday, Nicklaus said he had lunch with McIlroy in North Palm Beach, Fla., at the Bear's Club, the course Nicklaus founded and of which McIlroy is a member.
"He's gotten a lot bigger," Nicklaus said. "I said, 'Don't lift yourself out of a golf game.' He said he's really looking forward to getting started next year."
Both McIlroy and Woods will make their season debuts next month at the European Tour event in Abu Dhabi, United Arab Emirates.