"As of now, everything in that regard looks promising," said A's trainer Nick Paparesta. "We won't know until they get in to fix the fracture."
A surgery date has not been set. Parker will first go home, spend time with family and consult with specialists ahead of the imminent operation.
"We don't know how much this is going to set back his recovery at this point in time," said Paparesta, who later noted, "We have to figure out what the best option is to get this thing healed."
A potential third Tommy John surgery could be career-threatening. Rare is the pitcher who's able to throw at the big league level after going through the operation that many times. Former A's reliever Jason Isringhausen is one of the rare exceptions.
Before Parker suffered the setback Friday, when he clutched his elbow on his 87th pitch and collapsed on the mound while making his fourth rehab start for Triple-A Nashville, he was eyeing a return to Oakland's rotation by the end of the month. The A's were anxiously awaiting him, too, amid a stretch of inconsistent pitching.
A's manager Bob Melvin spoke to Parker earlier Saturday, before the pitcher's test results were known, and said, "Obviously he's a little bit down. You just try to be there for him and listen to him."
• Left-hander Sean Doolittle is tentatively scheduled to face hitters a second time Monday, as he continues rehabbing his throwing shoulder.
• First baseman Nate Freiman, sidelined early in Spring Training with a strained back muscle, was reinstated from the disabled list Saturday and optioned to Nashville.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.