Hays (calf) will begin a minor-league rehab assignment Tuesday, James Fegan of SoxMachine.com reports.
Hays has been out of action since landing on the 10-day injured list with a left calf strain in early May. He's already eligible for activation but will presumably need at least a few games to shake off rust. Jarred Kelenic has seen the bulk of the action in right field for the White Sox while Hays has been sidelined.