Spain's Rahm can overtake Dustin Johnson at the head of the rankings with a third PGA Tour win in this week's Farmers Insurance Open in San Diego.
But instead the world of golf is giddy with Woods' first full-field event since he retired hurt from the Dubai Desert Classic last February ahead of a fourth back operation.
Woods, now 42, underwent fusion surgery on his spine in April but returned to play in December's elite Hero World Challenge, appearing pain free and able to swing freely.
His fitness and level of play in finishing tied ninth of 18 in the Bahamas suggested the former world No.1's latest comeback has more substance than at the same stage last year.
"It's all finished now, it's fused and my quality of life is infinitely better than it was at this point last year," Woods told a pre-tournament news conference.
"My expectations have tempered a little bit because I haven't played.
"I just want to play on tour and get into the rhythm again. I'm going to grind it, give it everything I have. But I'm just trying to build toward April. I'm trying to play a full schedule and build for the Masters."
This time last year Woods had come through the Hero event unscathed after 15 months out following multiple back surgeries but missed the cut at Torrey Pines.
He then withdrew with back spasms after a first-round 77 in Dubai. Other than last year, this week's Farmers Insurance Open represents Woods first full-field event on the PGA Tour since August 2015.
However, Woods has some serious history at the Torrey Pines course. It was the scene of the last of his 14 major titles 10 years ago -- achieved on a broken leg -- and venue for seven other Tour titles.
On Tuesday, a relaxed-looking Woods played an early-morning practice round with Australian Jason Day, with whom he has forged a close friendship in recent years, and young American Bryson DeChambeau.
"This time he definitely looks ready," Day told reporters after their round. "I think his swing is really nice, he's hitting the driver a long way and he looks like he's got some speed, which is great. And his touch is coming back."
'Big question mark'
However, Masters champion Sergio Garcia, who has had a volatile relationship with Woods over the years,
sounded a note of caution over the American's return.
"It's going to be interesting to see," the Spaniard told a news conference ahead of his Dubai Desert Classic defence Wednesday.
"But, in my opinion, it's a big question mark to see how he's going to be able to do physically. I think that he looked pretty good at the Hero Challenge. But he has looked good at the Hero Challenge in the past and then, you know, he hasn't lasted too long."
'World No.1 bid'
Woods, who held the world No.1 spot for a record 683 weeks, only met Rahm for the first time this week.
The 23-year-old, who held top-ranking as an amateur for a record 60 weeks, has made a meteoric rise on the tour since turning pro in 2016.
This week marks only his 39th start as a pro -- victory, in the absence of top-ranked Johnson, would make him the second-quickest player to reach world No. 1 after Woods, who took 21 events to reach the top in 1997.
Rahm has yet to record a top-10 finish in the five majors he has played as a professional.
"The more attention you guys have on Tiger, the better for me, quite frankly," the PGA Tour reported Rahm as saying Tuesday.
"Hopefully I keep playing good and give you guys something to talk about, but it's not bad that the attention's on Tiger. It's good for golf, it's good for all of us."
The US-based Rahm overtook three-time major champion Jordan Spieth to reach world No.2 after clinching the CareerBuilder Challenge last week, following his breakthrough win at Torrey Pines last year. He has also won two titles on the European Tour.
He is the fourth Spaniard to reach second in the world after Seve Ballesteros, Jose-Maria Olazabal and Garcia. However Rahm would be only the second to reach No.1 after Ballesteros.
"It's hard to believe, to be honest, passing Jordan Spieth, three-time major champion, I only have two wins, he's got 10 plus, right?" Rahm told reporters after Sunday's playoff win in La Quinta, California.
"It's again, I said it many times, I never thought I was going to be at this point in my life right now, especially the way I won both victories, it couldn't be anymore different than the other."
Rahm will play alongside Day and Brandt Snedeker in the first two rounds, while Woods will accompany Charley Hoffman and US Ryder Cup star Patrick Reed.