But he may opt to delay that announcement until the conclusion of the BMW Championship, with the likes of Schauffele, Tony Finau and Kevin Kisner thought to be the most likely candidates for the 12th and final spot.
Play takes place in Paris, France, on September 28-30.
Eight other United States players made the roster after last month's PGA Championship after a two-year qualifying period - Dustin Johnson, Brooks Koepka, Patrick Reed, Justin Thomas, Jordan Spieth, Webb Simpson, Rickie Fowler and Bubba Watson. "I got the goose bumps when [Furyk] told me, and I'm excited to add my skills and talent to the team - a team that's stacked already".
Finau boosted his chances by joining a group that played at Le Golf National earlier this year.
Finau is one of seven players on the US team that is in his 20s. "I can play with anyone". And I let the guys on the team know that I'd be a great pick and I'd be ready to go. "And I'm playing some good golf, some world-class golf".
And that pick seems to be one of the toughest, coming down to either Tony Finau or Xander Schauffele. He was one of several players who received calls from the captain Monday afternoon thanking them for their efforts to make this year's team.
The Ryder Cup is now only a few weeks away from teeing off in Paris but the teams are still yet to be set.
"Hopefully I bring something to the team that can help us bring that Cup back".