The White Sox signed Dunn to a minor-league contract Friday that includes an invitation to spring training, James Fegan of SoxMachine.com reports.
Dunn will throw a bullpen session in front of scouts Tuesday in Phoenix, Jon Heyman of the New York Post reports.
Dunn (shoulder) elected free agency Wednesday.
Dunn (shoulder) cleared waivers and was outrighted to Triple-A Louisville on Monday.
Dunn will undergo surgery to repair a torn anterior capsule in his right shoulder, Mark Sheldon of MLB.com reports.
Dunn's rehab assignment at Triple-A Louisville was halted Thursday after he suffered a setback with his right shoulder, MLB.com reports.
Dunn (shoulder) is set to begin a rehab assignment Wednesday in the rookie-level Arizona Complex League.
Reds manager David Bell said Sunday that Dunn (shoulder) will work out of the bullpen once he's activated from the 60-day injured list, Charlie Goldsmith of The Cincinnati Enquirer reports.
Dunn (shoulder) threw a bullpen session Tuesday, MLB.com reports.
Dunn (shoulder) is targeting Aug. 8 as the date for when he'll resume facing hitters in live batting practice, C. Trent Rosecrans of The Athletic reports.