"If it feels like this tomorrow, we may have some problems," Dunn said. "But I'm anticipating getting better. I'm a quick healer."
Earlier Wednesday, White Sox manager Ozzie Guillen struck a cautious tone regarding Dunn's return.
"I talked to him this morning and he wants to play [Thursday]," Guillen said. "But I don't want to take the risk."
The good news for the White Sox is that Dunn, who began to feel discomfort in the abdominal area on Tuesday, won't be sidelined for long. He is expected to miss up to five games.
"With the trainers and doctors, baseball is staying on top of a lot of things right now," Guillen said. "In the past, you might be out for three months because they couldn't find out what it was. They might say it's an oblique muscle."
Dunn, who went 4-for-14 with one homer and five RBIs through the opening four games, hit into a forceout in the 12th inning of Tuesday's 7-6 loss to the Royals. He was lifted for a pinch-runner and medical officials determined after the game that the appendectomy was in order.
Guillen said Lastings Milledge and Mark Teahen would get more at-bats while Dunn is sidelined. Milledge started in left field Wednesday against the Royals.
Dunn, signed to a four-year, $56 million contract as a free agent during the offseason, had mentioned to teammates prior to Tuesday's game that something was bothering him.
"I'm glad they got it early," first baseman Paul Konerko said. "If you don't get on them early, those things can get bad. It sounds like he's going to be fine. He'll just be down a few days. We just have to pick up the slack and adjust while he's out."
Several Major Leaguers have undergone appendectomies in recent years -- including the Cardinals' Matt Holliday last week -- with varying recovery periods. The Giants' Andres Torres missed 12 days last September, while the Padres' Tim Stauffer missed two months between Major League starts last season and the Brewers' Corey Hart missed five weeks in 2009.
Holliday, who underwent the procedure on Thursday, is looking to return soon enough to be able to avoid a stint on the disabled list.