Dye and third baseman Josh Fields weren't in the starting lineup on Monday, as both were suffering from sore left hands.
The White Sox may be leading the Major Leagues in sore left hands -- at least it seems that way. And Guillen is piecing his lineup together with two regulars missing time.
"[Dye] is day-by-day. [He] feels better today, swung the bat a little bit," Guillen said on Monday. "Hopefully [he] will be ready to play tomorrow, or be ready to pinch-hit today."
Dye was hit by a pitch in the sixth inning against the Rangers on Saturday, while Fields was plunked during the first inning on Sunday.
Dye said it still was a little sore on Monday afternoon, but he'd continue to monitor its status throughout the night.
"I'll do soft-toss," said Dye, who was hitting .289 with six home runs in 23 games coming into Monday. "And then continue to get treatment today."
With Dye out, Guillen started Scott Podsednik in right field and inserted Brent Lillibridge in center field.
Fields' absence created another problem for Guillen, who started utilityman Jayson Nix at third base.
Entering Monday, Fields was hitting .256 with one homer and 10 RBIs in 23 games for the White Sox.
"It feels good," Fields said on Monday afternoon. "I got it X-rayed last night after the game -- it's not broken or anything. That's the best part."
But Fields said his wrist felt a little numb on Sunday after the game and it felt sore on Monday morning.
"Now, I guess it comes down to whenever I can feel like I can grip the bat with just a little bit of pain," Fields said.
Rustin Dodd is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.