Padres general manager Josh Byrnes said the prospect went back to San Diego on Tuesday for tests on his sore right elbow.
Padres manager Bud Black said on Wednesday no decisions have been made. No formal diagnosis was announced.
"The doctors are concerned about what the tests look like," Black said. "That's the best I can say."
Kelly is expected to get a second opinion on his right elbow and should make a final decision in a few days.
"There's going to be a lot of discussion between Casey and his family about all this," Black said. "I assume they'll want a second opinion to make sure all of their bases are covered. That's the right thing to do. We'd also want to make sure the proper course of action is taken."
Kelly was acquired from the Red Sox in the deal that sent first baseman Adrian Gonzalez to Boston in December 2010.