Davis (finger) is expected to throw a bullpen session Thursday, Adam Berry of MLB.com reports.
Davis joined the Pittsburgh rotation last week as a replacement for Nick Kingham, who was designated for assignment. He made it only three innings into his first start before developing a blister on his right middle finger that resulted in his placement on the 10-day injured list. Assuming the bullpen session goes well, Davis should get the green light to return when first eligible June 18 or shortly thereafter, but it's unclear if he'll have a rotation spot waiting for him.