Hall, 29, first came to the Major Leagues in 2000, and thus far in the season he has looked comfortable on offense and defense.
The Rays catcher is hitting .308 with four home runs and 12 RBIs; on defense he has thrown out seven of 29 would-be base stealers, and he has been aggressive with his arm.
Closer Danys Baez could be a candidate, but has not had many save opportunities.
Outfielder Carl Crawford is the other likely candidate after representing the Rays in the 2005 Midsummer Classic, but he would likely have to get on a hot streak to make a return trip.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.