Day’s International team take on the United States at the Jack Nicklaus Golf Club Korea in Incheon, South Korea, with the competition set to take place between October 8 and 11.
The Australian became world number one in September but was replaced by Spieth, who has won the US Open and the Masters in 2015, after just a week at the top of the rankings.
PGA Championship winner Day would relish the prospect of taking on Spieth in the Presidents Cup but knows that team tactics could see him miss out on the chance to face the 22-year-old.
Day, 27, said in a video published on The Guardian’s website: “I think it would be a lot of fun playing against Jordan, but then again I’m not too sure what their strategy is with that. If they’re going to hold Jordan to wait for my name or if captain [Nick] Price is going hold my name for Jordan.
“He may want me to go out early, try and get a point up. It all depends on where the points are.”
Day is joined by fellow Australians Adam Scott, Marc Leishman and rookie Steven Bowditch in the International team, with world number 88 Bae Sang-moon the only South Korean representative.