PITTSBURGH -- Pirates general manager Neal Huntington wants Major League Baseball to consider changing its concussion assessment system to allow for player re-entry after exiting a game for concussion testing.

Huntington offered the suggestion Sunday, a day after Pittsburgh catcher Francisco Cervelli suffered a head injury.

Cervelli was struck by the barrel of Joc Pederson's broken bat with two outs in the fourth inning. After being assessed on the field by a trainer, he remained in the game before removing himself in the bottom of the inning after briefly stepping into the batter's box.

Huntington said if a player knows he must leave a game to enter concussion testing, he's less likely to report symptoms.

"Any player that had an obvious concussion-risk incident should be allowed to be removed from the game, taken off the field, taken into the locker room, assessed by a doctor, assessed by a trainer, go through an extended period of time and then re-enter the game," said Huntington. "Because right now, all of this has to happen on the field."

Cervelli, 33, has a long history with head injuries during his 12-year career, with six documented concussions since 2011. He was placed on the seven-day concussion list Sunday.

"The player has to feel pressure as he's standing there with 30,000 or 10,000 or 50,000 eyes on him," Huntington said. "He has to feel pressure to make a decision whether [he's] in or [he's] out of this game. He knows if he takes himself out and he's the catcher, there's only one other catcher, and the game becomes a fiasco if that other catcher gets hurt."