The rankings would suggest it is Furyk's turn to take up the challenge but the 36-year-old makes it clear it is not a job he is interested in.
"As far as who anyone would pick to be the next guy to challenge Tiger, I would willingly beg you to pick someone else and please leave me alone, let me go do what I want to," Furyk said today ahead of the Masters starting tomorrow (NZT).
"I don't mind the attention, but I'm just fine and dandy going to a restaurant with my family and sitting down to a nice quiet dinner and enjoying it just as well.
"I think I get plenty of credit. I think that I'm not jealous of any of the due that anyone else in the golf world gets.
"And if for some reason you felt like I was a little underrated, it doesn't bother me.
"I'm comfortable with who I am, where I stand and what I'm trying to accomplish, and I don't really worry about the rest of it."
When Woods emerged as golf's dominant force, Garcia had looked the most suited to the role of his main rival but the fiery Spaniard has been unable to harness his immense potential and turn it into major championships.
Two-time Masters champion Mickelson and Vijay Singh, the workaholic Fijian, possess major credentials and enough defiance to stoke a healthy rivalry.
They have both exposed cracks in Woods' invincible persona but they have also been unable to pose a consistent threat to his domination.
Rankings aside, Furyk would seem an unlikely Woods rival.
Considered one of Woods' friends, Furyk has been paired with the 12-time major winner at Ryder Cup competitions, bringing very little edge to their relationship.
Furyk is also quick to point out that while he is No 2 in the rankings he remains a distant second (8.31) more than double the points behind the frontrunning Woods (20.16).
"At the time when Vijay overtook as number one, the points were probably a lot closer in the world rankings," Furyk said.
"Right now, I don't know the exact numbers but I want to say he has twice as many points as I do, more than twice as many ... so the gap is giant."
START TIMES
Tee times for the first round of the Masters at the Augusta National Golf Club tomorrow morning (All times NZT):
12:00am - Billy Mayfair, Ian Poulter
12:11 - Scott Verplank, Nick O'Hern, Joe Durant
12:22 - Larry Mize, Tim Clark, Troy Matteson
12:33 - Sandy Lyle, Dean Wilson, Bradley Dredge
12:44 - Ben Crenshaw, a-John Kelly, Davis Love III
12:55 - Chris DiMarco, Kenneth Ferrie, Steve Stricker
01:06 - Gary Player, a-Julien Guerrier, Vaughn Taylor
01:17 - Arron Oberholser, Niclas Fasth, Zach Johnson
01:28 - Tom Watson, a-Casey Watabu, Fred Funk
01:39 - Mark O'Meara, a-Dave Womack, Stuart Appleby
01:50 - Bernhard Langer, Rich Beem, Colin Montgomerie
02:01 - Chad Campbell, Angel Cabrera, J.J. Henry
02:23 - Mike Weir, K.J. Choi, Henrik Stenson
02:34 - Fred Couples, Geoff Ogilvy, Ernie Els
02:45 - Sergio Garcia, Bart Bryant, Shingo Katayama
02:56 - Phil Mickelson, a-Richie Ramsay, Adam Scott
03:07 - Jose Maria Olazabal, Charles Howell III, Justin Rose
03:18 - Stewart Cink, Todd Hamilton
03:29 - Seve Ballesteros, Carl Pettersson, Paul Goydos
03:40 - Ian Woosnam, Tim Herron, Robert Karlsson
03:51 - Jim Furyk, Rod Pampling, Ben Curtis
04:02 - Raymond Floyd, Miguel Angel Jimenez, Jeff Sluman
04:13 - Robert Allenby, Brett Wetterich, Lee Westwood
04:24 - Shaun Micheel, Jeev Milkha Singh, Ben Crane
04:46 - Craig Stadler, David Howell, Stephen Ames
04:57 - Retief Goosen, John Rollins, Yong-Eun Yang
05:08 -
MICHAEL CAMPBELL
, Lucas Glover, Rory Sabbatini
05:19 - Fuzzy Zoeller, Darren Clarke, John Edfors
05:30 - Mark Calcavecchia, Thomas Bjorn, Tom Pernice Jr.
05:41 - Padraig Harrington, Jerry Kelly, Luke Donald
05:52 - Tiger Woods, Paul Casey, Aaron Baddeley
06:03 - Vijay Singh, Brett Quigley, Hideto Tanihara
06:14 - Trevor Immelman, Camilo Villegas, David Toms
['a' denotes amateur]
- REUTERS