Cole (elbow) is expected to throw live batting practice Thursday, Bryan Hoch of MLB.com reports.
Thursday's session will be Cole's third against hitters and his first since throwing 30 pitches in a two-inning simulated game Saturday. There had been some talk after that session of the right-hander potentially next advancing to a minor-league rehab assignment, but it appears that isn't in the cards quite yet. Still, Cole seems to be progressing well in his recovery from right elbow inflammation and could be back in the Yankees' rotation by the the latter half of June.