"I will say that Tiger Woods is a great resource and would be a welcome to the team, whether that would be as a playing personnel or whether that would be as a vice captain," Furyk told a news conference in the French capital.
"He's been a great resource and a great person to have in the team room, so I'm hoping he will be part of that team.
The United States won the biennial match play event at home last October, marking their first triumph since 2008, but they have not celebrated on European soil since a 15-13 victory at The Belfry in England in 1993.
Former world number one Woods is hoping to make a return from multiple back surgeries but has been limited to only six competitive rounds in the past two years and would be a longshot to make the team as a player.
Furyk, nine times a player in the biennial competition who served as a vice-captain under Davis Love III at Hazeltine last year, tweaked the selection criteria and is placing a premium on in-form players.
Woods, who was part of the selection committee that named Furyk as captain in January, served as an assistant captain on the U.S. Ryder Cup team last year.
A few weeks ago the 14-times major winner, who has played in seven Ryder Cups but only in one winning team, admitted that he might never return to competitive golf.
Despite those doubts, he has being given clearance by doctors to resume full golf activity and on Sunday posted a video of himself hitting a drive on his official Twitter account.
"The swing that I saw on that video looked a lot like Tiger Woods. It reminded me of his swing of the past. It probably still needed a little speed. He probably still needs a little bit of golf strength maybe," said Furyk.
"But we really don't know when Tiger will be healthy. We really don't know when he'll return to competitive golf."
(Reporting by Frank Pingue in Toronto, editing by Pritha Sarkar)
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