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The pair, set to meet at this week's Abu Dhabi Golf Championship, have established a blossoming relationship since playing together for the first three rounds of last year's tournament and have expressed a mutual respect for one another's game.
But for a more heated rivalry to emerge, they both agreed they need to face each other on Sunday with a tournament at stake. It has yet to happen, although Woods did make a run at McIlroy in last year's Honda Classic with a birdie-eagle finish.
"It would be similar to saying that I had a rivalry with Phil (Mickelson) two years into my career. That wasn't the case. It takes time," Woods said on Tuesday.
"Over the course of my career, I've gone head-to-head against Ernie (Els) and Vijay (Singh), the most and that has happened over 17 years," he said. " But it takes time. Certainly we've done it once at Honda... But we really haven't had the amount of matches or head-to-head duals I've had with Phil and Vijay and Ernie. But then again it's only been a few years. Let's give it time and see how it pans out."
Speaking on Monday, McIlroy agreed.
"I don't know if you can call it a rivalry yet because we haven't battled each other down the stretch of a major," McIlroy said. "It's not like we've been playing in the final group of a tournament and we are battling each other. Hopefully at some point that can happen this year and it would be great to be part of that."
McIlroy joked that that the budding friendship would go out the window should that encounter take place.
"He is going to try and beat mine brains out. I know that," McIlroy said. "I'm trying to do the same. We are both trying to win a golf tournament."
Woods and McIlroy are paired together for the first two rounds at Abu Dhabi starting on Thursday.
