Woods won the last of his 14 majors in 2008, the year after McIlroy turned professional, but has been plagued by injuries and off-course problems since revelations about his personal life the following year.
The 40-year-old has not been a factor in any of McIlroy’s four major victories to date, missing the 2011 US Open through injury, finishing 69th in the 2014 Open and missing the cut in the US PGA a month later. Woods did finish 11th in the 2012 US PGA, albeit a distant 11 shots adrift of McIlroy.
Woods is currently sidelined after undergoing a third back operation in the space of 19 months in October, but although the odds are against it, McIlroy would love to battle the former world number one on the biggest stage.
“Hopefully if he can get healthy, I would still love to have a crack at him down the stretch in a major,” said the world number two, who moved above Jason Day in the rankings after the US PGA champion missed the cut in the Farmers Insurance Open last week.
“I would love that, just once.
“At this point it’s just up to him to get healthy and get his game back, and if I hopefully keep playing the way I’m playing, maybe one day it’ll happen.”
Before then, McIlroy has the small matter of defending his title in this week’s Omega Dubai Desert Classic to worry about, with a third victory the only acceptable outcome.
The 26-year-old claimed his first European Tour title at the Emirates Golf Club in 2009 and has also twice won the DP World Tour Championship a few miles away at Jumeirah Golf Estates, including to seal the Race to Dubai title last November.
“Leaving here with anything short of a win would be disappointing, of course it would,” said McIlroy, who is a combined 81 under par for his last six appearances in this event.
“Leaving any tournament without a win is sort of disappointing, but you try to put a positive spin on it.
“I think golfers, that’s what we usually do. We are disappointed for a bit and then we try to put positive spins on it, and the nice thing is there’s always a next week in golf.
“I’m sort of going for three in a row in Dubai with winning here last year and then winning the DP World Tour Championship at the end of last season, so it seems to bring out my best golf.
“I think this is my 10th year here - I played twice as an amateur - so I’ve got a lot of great memories and I get a lot of support here.
“There are a couple of little things that I took from Abu Dhabi (where he finished third) and worked on last week. So hopefully you’ll see my game just a little bit sharper and I’ll be trying to win for the third time to join Ernie Els as the only people to win three times.”
McIlroy will face some stiff competition from the likes of former Dubai resident Henrik Stenson, who won the Desert Classic in 2007 and also claimed the DP World Tour Championship in 2013 and 2014.
The 39-year-old finished joint third with McIlroy in Abu Dhabi in his first event since undergoing knee surgery on December 9, but pulled out of last week’s Qatar Masters after feeling the effects of his efforts.
“The knee is still attached, it’s moving forward and I’m lifting the leg,” joked Stenson, who has only finished outside the top 30 once in his last 11 visits to Emirates Golf Club.
“The previous two times I missed the cut in Abu Dhabi, which is never good fun, so I was very pleased with the week, both on the results side and how I played.
“I’m happy with the way things were going early doors and hopefully I can bring that into this week, too.”
Meanwhile Rickie Fowler believes following his victory in Abu Dhabi with a missed cut is “just a little hiccup” as he looks to get back on track this weekend in the Waste Management Phoenix Open.
Fowler’s dramatic win a fortnight ago was his fourth in the last nine months, starting with the Players Championship at Sawgrass last May in the week he and Ian Poulter were voted the most overrated players by their peers in an anonymous survey conducted by