Girardi rejected a suggestion that he could consider Rodriguez to fill in at shortstop in place of Jeter, instead of the tandem of Nix and Eduardo Nunez.
Rodriguez famously yielded shortstop to Jeter when he was traded to New York by the Texas Rangers before the 2004 season, but he actually made appearances in five games as a shortstop wearing pinstripes in '04 and '05, spanning eight innings.
"I have not seen him yet today, but even if he did volunteer, when is the last time he played there?" Girardi said. "So I don't think that's fair to do."
Sunday's Game 2 marked the first postseason game that the Yankees have not had either Mariano Rivera or Jeter on the active roster since Game 6 of the 1981 World Series, on Oct. 28, 1981.
Sunday marked Girardi's 48th birthday.