The 42-year-old ended the automatic qualifying race in 11th place, with the first eight after the US PGA guaranteeing a place in the side to face Europe in Paris.
However Woods, already named as one of captain Jim Furyk’s assistants, is a strong contender to be handed one of four captain’s picks after his resurgence this season, culminating in sixth at the Open and Sunday’s near miss behind Brooks Koepka at the US PGA.
At a news conference Monday, Furyk remained coy about the prospect of Woods getting a pick.
“He’s playing very well, there’s a lot of folks out there probably think he can help us,” said Furyk, a nine-time Ryder Cup star.
“I realize Tiger Woods is a story, I realize he’s playing very well and I’m excited to see that.”
Koepka tops the US Ryder Cup rankings after adding the US PGA’s Wanamaker Trophy to his second straight US Open title in June.
The 28-year-old will be joined in France by world No.3 Justin Thomas, top-ranked Dustin Johnson, Masters champion Patrick Reed, two-time Masters winner Bubba Watson, three-time major champion Jordan Spieth, Rickie Fowler and Players champion and former US Open winner Webb Simpson.
“This eight is exciting for any captain,” said Furyk. “They bring a lot to the table, and they love to compete. That’s what sticks out to me the most.”
Furyk will add three wildcard picks in September 4 and make a fourth selection on September 10 to bring his team to the final 12 to defend the title it won at Hazeltine 2016.
A 14-time major champion Woods made his Ryder Cup debut in 1997 and has played seven times in all but not since 2012. His record is played 33 matches, won 13, lost 17, halved three.
He was a vice captain for Davis Love two years ago and also reprized the assistant role at the Presidents Cup last year.
“He’s priceless, to be honest with you,” added Furyk, who admitted he would add another vice captain should Woods get a pick.
“He’s been really a big help to our captains in both 2016 and 2017 from a strategy perspective, from personnel, personalities, and also really serving on the golf course. I mean, walking with players.
“I think it’s been a big boost having the best player maybe to ever live following your group and being there for support.”
He added: “Tiger serves that purpose as a vice captain or a player and looking forward to having his help.”
In the build-up to the PGA, Woods said he was “trending” in terms of the wildcard debate after an impressive season given his recent history of four major back operations including spine fusion surgery last April.
After finishing two shots behind Koepka at Bellerive, he said: “I’m just very pleased at what I’ve done so far and now to be part of the Ryder Cup conversation, going from where I’ve come from to now in the last year, it’s been pretty cool.”
Woods is certainly box office. According to CBS Sports, ratings from Sunday’ saw a 69 percent increase compared to Sunday at Quail Hollow last year.
Woods’ fellow veteran Phil Mickelson is hoping for a wildcard that would give him a record 12th straight Ryder Cup appearance.
The 48-year-old left-hander was critical of Watson’s captaincy at Gleneagles in 2014, sparking a revamp of the US system which led to the revival at Hazeltine.
‘Going to be tough’
Furyk said he would be looking at a “body of work”, who is “hot” and how potential picks might fit in with his other eight players in terms of pairings for the foursomes and fourball matches.
He also said an ability to cope with what is likely to be a boisterous European crowd would be key, alongside a suitability for Ryder Cup venue Le Golf National.
“The Europeans know this golf course very well, they like it, they a have a lot of experience there and they have the home crowd,” added Furyk.
“I’m very excited about my team and I have a lot of confidence in my eight players but every one of them knows the task ahead of us and they know it’s going to be tough.”
The US last won the Ryder Cup on European soil in 1993 when Tom Watson’s side prevailed at The Belfry in England.
Europe has won six of the last eight editions of the biennial matchplay competition.
The European qualifying race ends on September 2 after which captain Thomas Bjorn will add four wildcards.
The Ryder Cup takes place at Le Golf National outside Paris, France from September 28-30.