13 first round draft choices have reached agreements to play for the team's who drafted them.
Norris is prepared to go anywhere at the trade deadline, but pitching for the San Francisco Giants would be a "dream come true" for the right-hander.
Putz is scheduled to throw for Triple-A Reno on Thursday and Saturday, and could rejoin the D'Backs by next week if all goes well.
The Phillies' second baseman will start his on-field recovery time Wednesday with the club's Double-A affiliate in Reading.
The right-hander's latest bullpen session was neck-pain-free, but Boston wants to give him a few extra days of rest before sending him back out to the mound.