Limited by injuries to 18 games during the regular season, Stanton homered in the series opener and missed the next two games because of a strained right quadriceps.
Stanton ran on the field before Thursday's game, but Boone already had made up his mind to keep Stanton out of the starting lineup.
"Probably for the first time saw some improvement today," Boone said. "Whether he's running at 60% or whatever, don't feel like he's ready to be an option in the field for us. I think there's a possibility of that kind of DH role now. So it's a little bit of a decision for me."
Boone said Stanton was available to pinch hit and could be New York's designated hitter for Game 5 on Friday night, a move that would cause him to either bench Edwin Encarnación or move Encarnación to first, with a resulting shift of DJ LeMahieu to third in place of Gio Urshela.
"I think outfield is still potentially in play moving forward, not yet," Boone said. "I would not feel great about throwing him out there yet in the outfield, and especially here in a big left field. When we get to Houston, temperature control, obviously a smaller left field, that may change a little bit."
Hicks was 0 for 2 with two walks in Game 3 on Tuesday, his first start since he injured his right elbow on Aug. 3.
"Just like him up in that spot as a guy that can potentially get on base a bunch and create traffic there at the top of the order," Boone said. "Having, again, three lefties in there tonight, just trying to keep the proper spacing as far as spacing our lefties and righties."
New York trailed 2-1 in the best-of-seven series going into Game 4 on Thursday, a day after rain forced a postponement.
LeMahieu was leading off and playing first, followed by right fielder Aaron Judge and Hicks in center. Second baseman Gleyber Torres hit cleanup, followed by Encarnación, left fielder Brett Gardner, catcher Gary Sánchez, Urshela and shortstop Didi Gregorius. Masahiro Tanaka was on the mound.
At 22 years, 308 days, Torres became the Yankees' youngest cleanup hitter in a postseason game, a mark that had been held by Joe DiMaggio at 23 years, 314 days in the 1938 World Series opener at Chicago's Wrigley Field.
Houston put Robinson Chirinos at catcher in place of Martín Maldonado and batting eighth and dropping right fielder Josh Reddick one spot to ninth.
George Springer was leading off, followed by second baseman José Altuve, left fielder Michael Brantley, third baseman Alex Bregman, first baseman Yuli Gurriel, DH Yordan Álvarez and shortstop Carlos Correa.
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