Furyk will add a final pick following the BMW Championship at Aronimink Golf Club on September 10.
At the time, Woods, 42, was ranked 656th in the world and had not earned a single Ryder Cup point.
Five-time major victor Phil Mickelson is also hotly tipped to be included for what would be a record 12th Ryder Cup - England's Nick Faldo is the only other player to compete in 11.
Woods, a 14-time major champion, and DeChambeau, coming off this third career PGA title at last week's Northern Trust event, are each expected to receive "wildcard" picks from USA captain Jim Furyk on Tuesday.
It was a disappointing day for Abraham Ancer, who had started the final round with a one-shot lead as he aimed to become the first Mexican player in 40 years to win a US PGA Tour title.
American Bryson DeChambeau held tough for his second consecutive FedEx Cup playoffs victory to ensure he will top the rankings heading into the US PGA Tour's season-ending Tour Championship later this month.
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And Congress, which has to approve any NAFTA rewrite, might refuse to endorse a deal that excludes Canada . Talks between the United States and Canada for revamping the trade deal, which includes Mexico, failed.
Phil Mickelson, who is also expected to earn one of Furyk's discretionary selections, also reminded the U.S. captain of his credentials with a magnificent closing day 63 for a 10-under-par overall total.
On Thursday fans get the chance to watch the official Opening Ceremony and then it's game on with both Europe and the USA's best players going head to head on Le Golf National's hallowed turf at one of golf's greatest events. "I'm very excited about the team this year". Perhaps Tony Finau, who's been in strong form lately, is most likely to be Furyk's final pick. The idea is to find the hottest player to fill out the team, and no one has been close to DeChambeau over the last two weeks. The U.S. has not won a Ryder Cup on European soil since 1993, when it won at the Belfry in England. Check in for highlights from every tournament plus player interviews, player profiles, tournament previews, swing analysis and all the greatest shots and fantastic moments.
Furyk said Woods will no longer serve as a vice captain.
Thomas Bjorn has selected Ian Poulter, Henrik Stenson, Sergio Garcia and Paul Casey as wild cards for his European Ryder Cup team, it was announced Wednesday. Woods was an assistant at Hazeltine and at the Presidents Cup last fall at Liberty National in a US route.