"We're looking at probably four [rehab games] right now," Melvin said.
Reddick suffered a right wrist injury that ultimately put him on the disabled list May 8. He took more than 20 batting-practice swings in Houston on Friday and said he "felt great."
Oakland plays the Giants in San Francisco on Wednesday and Thursday, before hosting the White Sox for a three-game set beginning Friday.
Willie Bans is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.