Fourteen-times Major winner Woods believes it will take time to develop the same sort of rivalry with world number one McIlroy that he has experienced with the likes of Phil Mickelson, Vijay Singh and Ernie Els.
"I think I've gone head-to-head against Phil, Ernie and Vijay the most over the course of my career," the former world number one told reporters at the Abu Dhabi Golf Club on Tuesday.
"For something like 16 or 17 years we've been going at it like that but it takes time. Rory and I haven't really had the amount of head-to-head duels that I've had with Phil, Vijay and Ernie ... so let's just see how it pans out."
While Woods was keen to play down the competitive nature of his rivalry with McIlroy, the duo have clearly built a strong bond since they were paired together in Abu Dhabi 12 months ago.
"It started here last year," said the 37-year-old American. "I played the front nine with him in practice on the Tuesday and we were paired together on the first three days too.
"Our relationship has grown since then," added Woods who finished joint third behind surprise British winner Robert Rock in the 2012 Abu Dhabi Championship. "We've hit it off and our friendship's gotten better."
World number two Woods and McIlroy will again play together in the opening round of this year's tournament, along with triple former Abu Dhabi champion Martin Kaymer, on Thursday.
The Florida-based American said he was expecting to spend even more time in McIlroy's company when the 23-year-old Northern Irishman finally moved into his new US home.
"Having him in Florida I'm sure we'll have a few dinners together and certainly hang out a bit more," said Woods.
McIlroy, who last year added the US PGA Championship title to the US Open he won in 2011, also spoke of the friendship he had forged with Woods since finishing second behind Rock in Abu Dhabi.
"We have spent more time together," said the Northern Irishman. "Before this time last year we would say hello in passing but not really anything else.
"I think once Tiger sort of gets to know you and trusts you and let's you in, it's great.
"We get on really well, we share the same interests and we are both big sports fans. The bulk of our conversations are about sport."
McIlroy joined Woods in the Nike stable on Monday after signing a new deal with the US sportswear firm that, according to media reports, will be worth $250 million over 10 years.
With demands growing on McIlroy's time with every new contract and every new tournament victory, the young Northern Irishman has been grateful to be able to turn to Woods for the occasional spot of advice.
"I've asked him about time management and practice and how he likes to do things and the structure and the setup around him," said the world number one.
"At one point last year I felt like I wasn't getting the time I needed to go and do my practice. There were so many commitments and everything else.
"He has had to deal with that more than anything else so it has been good to chat about that stuff."
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