"If he continues to be healthy, which we expect, then we'll activate him," A's manager Bob Melvin said.
Prior to joining the River Cats, Norris said the only baseball activity that caused him trouble was running at full speed, while running, cutting, swinging and squatting were fine.
The pain is manageable, he said, crediting his high tolerance for pain.
"It depends on where the break is," Melvin said. "He's obviously able to handle it right now. As far as his pain tolerance, I'm not really sure on that. If he says that, I believe him. Most catchers are."
With rosters having expanded, Norris' return will make him the fourth catcher on the roster with recent acquisition Kurt Suzuki, Stephen Vogt and John Jaso, who is on the DL with a concussion.
"I really don't' know yet," Melvin said about any pending roster moves. "Like most things we do, we try to match up the best on a particular day."
Jeff Kirshman is an associate reporter for MLB.com. Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.