Furyk will make his fourth captain's choice selection at the conclusion of the BMW Championship, which is being held this week at Arnonimink Golf Club in Newtown Square.
Woods will return after missing the past two Ryder Cups with a long-standing back injury.
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.
The three will join the eight players who previously earned automatic spots on the USA team that will take on Team Europe at Le Golf National in France beginning September 28.
U.S. Ryder Cup captain Jim Furyk made three of his four captain's picks Tuesday, leaving just one spot open on the 12-man roster.
2018 Form: Cabrera-Bello has picked up six top-ten finishes whilst splitting his time between the PGA and European Tours, and he gave Bjorn a timely reminder of his abilities when tying for 7th in what was a loaded field at the Dell Technologies Championship last time out.
Still to come for Furyk is his final captain's pick, to be announced Monday after the BMW Championship.
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Bryson DeChambeau has netted a small fortune in just two weeks, with a stunning season-first on the PGA Tour sealing him a special piece of golf history.
That seemed like a pipe dream, but as Woods played and quickly began contending in tournaments, it began to look like a reality and was cemented by his runner-up finish at the PGA in August.
"But also deep down I wanted to make the team".
Tony Finau is believed to be the leading candidate for 12th and final spot. "It's going to be an interesting crowd".
Brooks Koepka, Dustin Johnson, Justin Thomas, Patrick Reed, Bubba Watson, Jordan Spieth, Rickie Fowler and Webb Simpson were the eight automatic qualifiers for the American team, with Furyk's picks the three immediately below them in the qualification standings. "How much? I would say it depends on what I can do in the restrictions of my biomechanics". He is a former U.S. Amateur champion and has already developed a bond with Woods, looking to speculation about a possible pairing in France.
"He has been instrumental, not only in helping the captains before me, but me as well", Furyk said. He named David Duval, Zach Johnson and Matt Kuchar as assistants to join previously announced vice captains Davis Love III and Steve Stricker.