Volquez (13-7, 3.04 ERA) finished the regular season having not allowed a run in a career-high 18 consecutive innings. He also posted a 1.08 ERA in September -- the second-lowest among National League pitchers.
"To pitch that game would be something really big for me," Volquez said Sunday.
The Pirates, who will be playing in the wild-card game for the second consecutive season, will host the Giants at PNC Park on Wednesday. The winner will face the Washington Nationals in the division series.
The Giants had already announced that left-hander Madison Bumgarner would start the wild-card game.
Volquez led the Pirates in wins, ERA and innings pitched (192 2/3) this season.
The Associated Press contributed to this report.