Manager Clint Hurdle said before Friday's game against the Chicago Cubs that Rodriguez has no "acute structural damage to the ligament" in his throwing arm. Even so, the Pirates will wait to see how his arm responds during Monday's session before making a decision.
Rodriguez recorded only one out in Pittburgh's 5-0 loss at Atlanta on Wednesday before leaving with tightness in his left forearm.
After the game, he returned to Pittsburgh and was examined by doctors.
Rodriguez is 6-4 with a 3.59 ERA in 12 starts. He left a game on April 8 at Arizona with a left hamstring strain and missed one start.