Furyk will name his final pick on Monday, following this weekend's penultimate PGA Tour event, the BMW Championship.
However Woods' form since his return to golf this year prompted Furyk to award him one of the four captain's picks set aside for players who did not qualify automatically for the team. Mickelson, who has played on every Ryder Cup team since 1995, boosted his case by winning a World Golf Championships event in Mexico in March, and he made nine birdies Monday in a closing round of 63.
The first three captain's picks made by U.S. Ryder Cup captain Jim Furyk on Tuesday turned out to be about as surprising as the Jets naming of rookie Sam Darnold as their starting quarterback.
DeChambeau earned a spot on the team thanks to three wins this year (Memorial Tournament, The Northern Trust and Dell Technologies Championship).
Furyk announced 14-time major champion Tiger Woods, Phil Mickelson and back-to-back PGA Tour victor Bryson DeChambeau will compete in France to help the US defend its title. The Dane has some hard decisions to make before he announces his final four team members and we have analysed his potential captain's picks ahead of the announcement at 2pm on Wednesday 5 September.
The matches are September 28-30 outside Paris. Check in for highlights from every tournament plus player interviews, player profiles, tournament previews, swing analysis and all the greatest shots and incredible moments. 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.More news: Serena marches on after battle with gritty Kanepi
More news: Celtic rumour mill: Reaction to Hoops victory over Rangers
More news: Russia had Trump ‘over a barrel’, claims former British spy
Tony Finau is believed to be the leading candidate for 12th and final spot. "We're heading over to Europe, where it's going to be an interesting, boisterous crowd". "How much? I would say it depends on what I can do in the restrictions of my biomechanics".
"But also deep down I wanted to make the team". Woods was an assistant at Hazeltine and at the Presidents Cup last fall at Liberty National in a USA route.
"He has been instrumental, not only in helping the captains before me, but me as well", Furyk said.