White Sox manager Robin Ventura says Dunn could pinch hit, but the injury is still not where it needs to be for him to play an extended role. Chicago is trying to hold on to a one-game lead in the AL Central over the Detroit Tigers -- with Justin Verlander pitching against the White Sox on Sunday night.
Dunn, who leads the majors with 38 home runs this season, spent the day receiving treatment from trainers Herm Schneidner and Brian Ball.
"It definitely feels better today than it did on Friday," Dunn told ESPNChicago.com's Bruce Levine. "Treatment-wise we have hit it pretty hard over the last few days. I think it has helped, but I really won't know until I swing again."
Dunn suffered the injury while attempting to hold up his momentum on a check swing Wednesday. He will try to take some swings in order to make himself available for late-inning pinch-hitting opportunities Sunday.
"I probably won't swing today unless later in the game, if we need something," he told Levine.
The White Sox welcomed back outfielder Alejandro De Aza, activated from the disabled list Sunday. He had been out with bruised left ribs.
De Aza is in the starting lineup, hitting leadoff and playing center field.
ESPNChicago.com's Bruce Levine and The Associated Press contributed to this report.