He simply hopes his countrymen don't cheer for the reigning Masters champion.
Woods will be making his first playing appearance in Australia since competing in the 2011 Presidents Cup, and Scott hopes his International team can enjoy more of an advantage away from the United States.
"Last time it was too friendly," Scott told the Herald-Sun in Melbourne. "Quite bluntly, we want the home-crowd advantage, and I'll be disappointed if they are cheering enthusiastically for Tiger or anyone on the U.S. team."
Scott has never played on a winning International side and has been part of seven defeats in the Presidents Cup. The only International victory came at Royal Melbourne in 1998.
Woods will be a playing captain for the U.S. side that is heavily favored.
"I'm not saying be a poor sport, but one challenge our team has always had is gaining a home-soil advantage because it's rare that stars like Tiger and DJ [Dustin Johnson] come to Australia (2011) or Korea (2015) where we play these things and the locals are excited to see them as much as anyone on our team," Scott said. "But while we appreciate them very much, we don't have to cheer for them."
Scott is playing at this week's Australian Open while 11 of the 12 Americans, including Woods, will be in the Bahamas for the Hero World Challenge.