Murfee (elbow) threw a bullpen session Tuesday in Oakland, Chandler Rome of The Athletic reports.
Murfee has been slowly working his way back all season from Tommy John surgery that he underwent last July. Manager Joe Espada said that the right-hander could throw one more bullpen session before beginning a minor-league rehab assignment. Murfee will likely need to make a series of appearances while on his rehab assignment, but if all goes well, he could make his return to the major-league roster at some point in mid-to-late August.