McIlroy, who finished second on Sunday at the Valero Texas Open after a tumultuous start to his 2013 season, will play in his fifth Masters this week at Augusta National, where his best finish is 15th in 2011.
"I don't see myself a rival to Tiger or to anyone,'' McIlroy said Tuesday morning prior to a practice round at Augusta National. "His record, when you speak of rivals ... you tend to put rivals who have had similar success. He's got 77 PGA Tour (wins); I've got six. He's got 14 majors; I've got two. If I saw myself a rival to Tiger, I wouldn't really be doing him much justice.''
Woods, on the other had, said he felt a challenge from McIlroy.
"I think that over the course of my career, I've had a few," Woods said. "You know, certainly Rory is this generation. I've had Phil (Mickelson) and Vijay (Singh) and Ernie (Els) and David (Duval) for a number of years, and now Rory's the leading of this new, younger generation. So yes, definitely."
Woods has won three times this year and two weeks ago went back ahead of McIlroy to the No. 1 ranking with hopes of winning his 15th major championship -- and first since 2008 -- this week.
Nonetheless, there is clearly a good bit of attention following McIlroy, 23, wherever he goes. He won five times worldwide in 2012 and was the player of the year on both the PGA Tour and European Tour, winning money titles on both circuits.
And he won his second major championship, capturing the PGA Championship at Kiawah by eight strokes.
That increased expectations for 2013, which has seen him sign a lucrative endorsement deal with Nike, make a significant change in equipment, and then struggle with a missed cut in Abu Dhabi, a first-round exit at the WGC-Accenture Match Play, and then a controversial withdrawal from the Honda Classic.
McIlroy began to find his form at the WGC-Cadillac Championship, and last week's event in San Antonio has given him a boost of confidence coming here.
"I got what I wanted out of it in terms of playing more competitive golf, getting the scorecard in my hand, shooting scores," he said. "I think a bonus was getting into contention, and I felt like how I played when I got into contention was really pleasing. I chased Martin (Laird, the tournament winner) down pretty hard on the back nine. Most Sundays, when you shoot 66 in these conditions, it's going to be enough. I just gotten beaten by an unbelievable round (63). I got a lot out of last week."
In adding Texas to his schedule, however, McIlroy had to cancel a planned visit to Haiti, where he went two years ago prior to the U.S. Open, gaining some perspective in the wake of the devastating earthquake.
"It was tough, because golf sometimes is a selfish sport, and sometimes you have to do what's right for yourself,'' he said. "I knew I was letting a lot of people down with my decision to go to San Antonio, but at the end of that day, that's what I needed to do to feel like I was ready for this week and this tournament.
"I made a couple of tough phone calls. But I felt like it was the best way for me to prepare for this week.''
McIlroy again proclaimed that the issues in his golf game have had nothing to do with the Nike equipment, but with a flaw in his golf swing that he believes is corrected.
And he noted that he went through a rough period last summer, missing the cut in four of five tournaments, before getting on a roll late in the year.
"I've went through these sort of patches before where I haven't played so well and the game feels quite far away, and then something clicks and then all of a sudden it's back again,'' he said. "I probably should have learned more from it last summer when I was going through those struggles, but it's just about keeping on top of everything, keeping on top of the fundamentals.
"When I don't play my best, it's when I get into bad habits in my golf swing. Whenever my golf swing is where I want to be, that's when I produce results, and that's what I've seen has started to happen over the past few weeks."
McIlroy, who said he was so in awe of Augusta National when he played it for the first time in 2009 that it "took me a while to get comfortable taking a divot,'' said he will employ a slightly different strategy this year.
"Try to hit it into the fat parts of the fairway,'' he said. "Because I'm confident with my iron play, so there's no point in taking on too much off the tee. There's generous fairways out there, and you hit it on the fat parts and you're always going to give yourself a good chance to get it close to the pin.''
McIlroy said he will participate in Wednesday's Par-3 Contest with tennis star and girlfriend Caroline Wozniacki caddying for him.