The first baseman says he hopes to play Tuesday when the White Sox meet Minnesota.
Konerko underwent tests Friday that revealed no major damage after being hit by Jeff Samardzija. Konerko had a black eye and a cut near his nose hours before the first pitch Saturday night at Wrigley Field.
"I woke up this morning and it was completely shut. I knew it would be because you can't ice it through the night," Konerko said. "But since I got here there has been a lot of improvement as far as how wide I can open it and how much I can see out of it."
"It's just a matter of time. It can be later today, it can be tomorrow, the worst case would be Tuesday," he said. "I don't really have that much soreness up in that area. There are no other symptoms except what you guys see, so that's good."
Konerko homered in the first inning Friday and then was hit by a high pitch in the third inning. Adam Dunn started at first Saturday night.
Konerko did not feel the pitch was intentional.
"I thought it looked like a cutter, a slider from the front end. I think he said it was a splitter, so obviously it didn't come out right," Konerko said.