"We got to wait five days. I have to," manager Ozzie Guillen said. "Every day he feels better and better. I don't expect him to be back in five days, to be honest with you."
Dunn said he wants to continue taking things day by day. He was out of the lineup for the third straight game Friday against Tampa Bay.
"I'd rather lose a game than lose a guy for another month,"Guillen said. "If I have to pinch-hit Adam Dunn with the game on the line, I'd rather lose the game rather than have him hurt himself and lose him for we don't know how long."
Dunn is hitting .286 in four games for the White Sox this season. He has one home run and five RBIs. Chicago signed the slugger to a four-year, $56 million contract in December.
"He's got to hit [in batting practice], he's got to show me, he's got to show the doctors, the trainers, [GM] Kenny [Williams], he's got to show a lot of people," Guillen said. "He's got to show his hitting coach. When everybody says he's ready, he's in the lineup. Obviously we want him in the lineup but we got to be careful."
Information from ESPNChicago.com's Doug Padilla and The Associated Press was used in this report.