Iglesias (shoulder) will throw either live batting practice or in a minor-league rehab appearance Thursday, David O'Brien of The Athletic reports.
Iglesias was able to face live hitters for the first time Monday and is now scheduled for at least one more round of work. It's unclear how many rehab appearances Iglesias will make should he go on an assignment, but he figures to be very close to the end of his recovery process and could even return as soon as this weekend.