Team USA first baseman Mark Teixeira of the New York Yankees withdrew with a right wrist injury, and Konerko is on a contingency list of players who agreed to be considered as replacements. The list also includes first base candidates Prince Fielder and Ryan Howard.
The White Sox previously signed off on allowing Konerko to participate in the event if chosen.
“It is his decision,” Sox manager Robin Ventura said. “He has been around long enough to know if it would help him get ready for the season.”
Konerko, who turned 36 on Tuesday, had wrist surgery in October 2012. The Sox team captain said he has 100 percent healthy since a month after the wrist procedure.
Konerko had three hits on Tuesday against Team USA in a 4-4 tie.