Kopech allowed two walks and struck out one across a scoreless ninth inning in the second game of Tuesday's doubleheader against the Nationals.
Kopech registered a save against the Rays on Wednesday, allowing one hit in one scoreless inning.
Kopech (1-3) threw a scoreless ninth inning while allowing one walk and striking out one to earn the win Saturday against the Cardinals.
Kopech allowed two earned runs on two hits and no walks while striking out two to earn a hold Tuesday against the Twins.
Kopech (0-2) blew a save and ultimately took the loss in Wednesday's opening game against Kansas City, allowing two runs on two hits while striking out one.
Kopech (0-1) allowed one earned run on one hit and two walks while striking out three to take the loss Friday against the Royals.
White Sox general manager Chris Getz said Thursday that Kopech will begin the season in the bullpen, Scot Gregor of the Chicago Daily Herald reports.
Kopech (knee) threw a bullpen session Wednesday and doesn't appear to have any limitations on the White Sox's first day of spring training, Daryl Van Schouwen of the Chicago Sun-Times reports.
Kopech (knee) agreed to a one-year, $3 million deal with the White Sox on Thursday, avoiding arbitration, Daryl Van Schouwen of the Chicago Sun-Times reports.
Kopech was placed on the 15-day injured list Friday with right knee inflammation.