While Bjorn could have as any as 10 genuine contenders from which to select his four wild cards tomorrow, Furyk looks set to opt for Bryson DeChambeau, Phil Mickelson and Tiger Woods, the players who finished ninth, 10th and 11th in qualifying.
It is only the identity of his final wild card, to be named after the third FedEx Cup play-off event on September 10, which will be causing Furyk a headache with the likes of Xander Schauffele, Matt Kuchar, Tony Finau, Kevin Kisner and Zach Johnson in the frame.
Woods underwent spinal fusion surgery in April last year and was arrested on suspicion of driving under the influence the following month when he was found asleep at the wheel of his car.
Woods only returned to competitive golf in November but has been impressive ever since, recording five top-10 finishes and missing just two halfway cuts, with sixth place in the Open at Carnoustie and second in the US PGA removing any lingering doubts about his place on team.
The 14-time major winner will be replaced as a vice-captain when selected. His last Ryder Cup appearance was six years ago.
Mickelson is having to rely on a wild card for the first time in his career after his chances of qualifying ended with a missed cut in the US PGA, although the left-hander did win his first title since the 2013 Open in the WGC-Mexico Championship.
DeChambeau also missed the cut in the US PGA but has won twice on Tour this year including last week in first round of the FedEx Cup play-offs.