Stricker, who along with Woods was an assistant to U.S. captain Davis Love III for last week's winning Ryder Cup effort at Hazeltine National, also named Love and Fred Couples as assistants for the competition, which pits a U.S. team against an international squad of players from outside of Europe.
"Tiger certainly could play his way onto the U.S. team, and if that happens, replacing him as a captain's assistant will be a great problem for me to have," Stricker said. "But if he doesn't, I'm honored he accepted this role for the first time in his impressive Presidents Cup career. Tiger has been a great teammate and friend over the years, and I know the U.S. guys will benefit from the experience and camaraderie that only Tiger can bring."
Woods said Sunday at Hazeltine that he enjoyed his time as an assistant for the U.S. team and would consider being a captain in the future. Woods is 24-15-1 in eight appearances as a player in the Presidents Cup.
The U.S. has nine victories in the 11 Presidents Cups played. They lost in 1998 and tied in 2003.
Stricker was an assistant captain for the U.S. Ryder Cup team in 2014 as well as the Presidents Cup in 2015. He is a strong contender to be a U.S. Ryder Cup captain in the future.
The competition will take place over four days, Sept. 28-Oct. 1.