The world number one and two, who played together for the first three rounds of last year's tournament, will resume their competitive challenge at the National Course on Thursday.
Both men have tried to play down any claim of it being a rivalry yet, having taped a TV commercial for Nike together ahead of McIlroy's unveiling in Abu Dhabi last night.
"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.
"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.
"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 duels 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.
"We've certainly hit it off, and our relationship has grown and our friendship's got better. Certainly give each other the needle quite a bit. That's always fun."
The pair have been developing a friendship off the course over the last year, McIlroy admits, though that will go out the window on the National Course if both men are chasing the title.
"Before this time last year, we would say hello in passing but not really anything else," said McIlroy.
"It's great to just spend time with him and pick his brain about a few things if I feel I need to. It's a relationship that's definitely based on respect, because you know, he's been a huge hero of mine growing up and he's done some incredible things in golf.
"I think he respects me for what I've done on the golf course, too. So it's good."