Furyk, who will be 48 when the biennial matches head to Le Golf National in Paris, played on nine straight Ryder Cup teams from 1997-2014, compiling a 10-20-4 individual record. He also served as an assistant last year at Hazeltine, where the U.S. defeated Europe for the first time since 2008.
While Furyk nearly made the most recent team on merit and shot a PGA Tour-record 58 at the Travelers Championship in August, he indicated at the RSM Classic in November that he would accept the captaincy if offered.
"If they decide in '18, '20, '22, whenever it is, if they decide that I'm the right person, I would love to have that job," Furyk told the Associated Press. "I think everyone would."
According to the Telegraph report, the choice came down to Furyk and Fred Couples, who has won the Presidents Cup three times as a captain but has never led a Ryder Cup squad. The committee choosing the 2018 captain includes Tiger Woods, Phil Mickelson and the most recent captain, Davis Love III.
Denmark's Thomas Bjorn was selected as European captain last month. Should Furyk be chosen, he'll attempt to become the first U.S. captain to win the matches on foreign soil since Tom Watson led the 1993 squad to victory at The Belfry in England.