Dunn, who is dealing with a strained right oblique, missed his seventh straight game on Friday. He originally sustained the injury in Baltimore during the last week of August.
He took batting practice prior to Friday's game for the first time after doing some cage work earlier in the day.
"When I swung today, it felt fine," Dunn said. "Going to take batting practice and you know, swing normal. Let it eat and see how it goes today. The plan is to be in there tomorrow."
Dunn said he initially returned too quickly from the injury, playing a game in Detroit and three against Minnesota earlier this month.
As a result, White Sox manager Robin Ventura is understandably not as eager as Dunn to say he'll play on Saturday.
"I watched him swing [in the cage] a little bit today," Ventura said. "I want him to get out here and swing in a controlled BP session. Once you get in a game ... it becomes different. He can swing it. It's just I'd rather get him out here [for BP].
"It's probably looking like tomorrow or Sunday for him to play."
Even when Dunn is healthy enough to return, that won't necessarily mean he'll be 100 percent. That likely won't come until the offseason.
"If this is in April, I'm probably going to give it as much time until it feels really good," Dunn said. "I don't have that luxury if I want to play again [this year]. If I wait till it felt 100 percent, then we'd have to play probably until Thanksgiving. I don't see it feeling 100 percent.
"As long as it's healed up to where I'm not going to get back to where I was a week ago, then I'm fine. Let's do it."