Even if given a clean bill of health, with 18 days until the season begins, neither is likely to be ready.
"We're two weeks away from the season and they're both in jeopardy of not starting with us," manager Bob Melvin said. "We're not, even if completely cleared in evaluation, running them out there his next time. Potentially it's a couple of blows for us. But that's why we have the depth that we have."
Tommy Milone, long considered a sixth starter, and Jesse Chavez would be in line to fill out the rotation after Sonny Gray, Scott Kazmir and Dan Straily.
"We'll have somebody else step up if they're not ready. That's all it comes down to," Straily said. "We're not limited to five quality arms in this organization. We probably have seven, eight, nine quality guys who are big league ready right now to be starters."
Chavez already was knocking on the door to crack the rotation. He has not allowed a run in 10 2/3 innings this spring. The left-handed Milone has a 6.00 ERA and three home runs allowed in nine innings.
"We have Tommy Milone, and Jesse Chavez is pitching really well right now, too," Melvin said. "Again, until final evaluations with what's going on with these two guys, we're very comfortable with Milone and Chavez."
Parker had forearm issues last season as well and had Tommy John surgery in October 2009 while in the Diamondbacks' system. Andrews performed that surgery and Parker returned to the mound in April 2011.
Parker, who was the favorite to get the Opening Day start, did not fare well in either of his first two spring starts and Melvin noticed something was off as Parker played catch on Thursday.
"I called him in and we talked," Melvin said. "He admitted to me that his forearm is a little bit tight. So we're going to be proactive and take care of that as soon as we can."
Melvin said the team will have Griffin's MRI results on Saturday.
Griffin gave up five runs on nine hits in 3 2/3 innings Thursday night against the Rockies, which raised his spring ERA to 10.38, but he said afterward his arm felt good.
Griffin has never had elbow issues in his professional career but went on the disabled list in 2012 with shoulder tightness. Griffin missed the playoffs last year, though Melvin on Friday said it was because the right-hander had run out of gas instead of a specific injury.