Gallen (hamstring) threw a flat-ground session Saturday and is expected to throw a bullpen session soon, Jesse Friedman of GoPHNX.com reports.
Gallen was cleared for throwing June 3 and was able to complete a flat-ground session Saturday. The next box for Gallen to check in his recovery from a right hamstring strain would be a bullpen session, which should occur in the coming days. Gallen will be eligible to return from the 15-day injured list June 15, though it's unclear if he'll be ready to join the big club by then.