White Sox general manager Chris Getz said Tuesday on MLB Network Radio on SiriusXM that Taylor will move into the rotation next season.
Burke was charged with the loss in Game 5 of the ALDS against the Guardians on Saturday, giving up two runs on four hits with four strikeouts and no walks over five innings.
Trammell is not in the lineup Wednesday for Game 2 of the wild-card series against the White Sox.
Paredes (knee) will start at designated hitter and bat third Wednesday in Game 2 of the wild-card series versus the White Sox.
Smith didn't factor in the decision in Game 1 of the AL Wild Card Series against the Astros on Tuesday. He allowed two hits with one strikeout and no walks over three innings.
Varsho underwent arthroscopic surgery on his left wrist Tuesday, Matt Kawahara of the Houston Chronicle reports.
Okert (hamstring) is not included on the Astros' wild-card roster against the White Sox, Chandler Rome of The Athletic reports.
Meidroth (hamstring) will start at second base and bat eighth Tuesday in Game 1 of the American League Wild Card series in Houston.
Pecko has been dealing with a left hip issue and is not on the Astros' roster for their AL Wild Card Series versus the White Sox, Chandler Rome of The Athletic reports.