Konerko, who sustained the concussion against the Royals on Tuesday, is progressing well and will start doing some light physical activity as early as Tuesday.
White Sox manager Robin Ventura said the plan is for Konerko to start riding a stationary bike and incorporate some running but doesn't expect him to start doing any baseball activities other than take grounders and maybe play catch until later in the week.
"I would imagine once he starts doing baseball stuff, [the doctors] will check him to make sure [the concussion symptoms] go away," Ventura said. "Right now, it's slow stuff. Most of it is just rest."
Konerko, who did not travel with the team to Toronto, is eligible to come off the seven-day disabled list Friday when the White Sox are in Kansas City. Ventura said everything would have to be perfect for that to happen and that it's too early to tell if that scenario is likely.
"It's just more of how he feels," Ventura explained. "You have seen some guys, it takes them a long time to get back and some guys where it hasn't taken that long. Gotta cross your fingers, hoping it's Friday."
While Chicago will certainly miss Konerko's middle-of-the-order production, Ventura said his leadership qualities in the clubhouse cannot be overstated.
The skipper described Konerko as a lead-by-example type of player, rather than a vocal leader, but said he still commands the attention of his teammates
"When people think about the White Sox, he's going to be the first thing you think of because of his tenure, stature on the team and the way he does things," Ventura said. "He does things the right way.
"There is just the example he sets on how guys act, prepare and play the game."
In 101 games, Konerko is batting .316, with 18 homers 54 RBIs and an .892 OPS.