Girardi said he'd like to get Granderson a half-day off sometime in the next three days by playing him at designated hitter.
"He's been a guy, though, who hasn't really needed them in the past," Girardi said. "He's been able to play every day, but I've talked to him a couple times this week to see if he's been OK, and he's been OK."
The Yankees have an off-day on Thursday before traveling to Oakland, and Girardi hoped that would help give his center fielder a rest. Granderson isn't new to playing on little to no rest. He said he's played every game with few off-days for the bulk of his career, and he doesn't feel tired or worn down this season.
"It's part of it, you get yourself ready to play regardless," Granderson said. "We've had scheduled days off, so it's not like I haven't had any rest. It's one of those things where if you get it, great. If not, get ready to play."
Granderson is one of seven players who have appeared in every inning of his team's games this season, joining Seattle's Ichiro Suzuki, Baltimore's Adam Jones, Atlanta's Dan Uggla, Philadelphia's Shane Victorino, the Cubs' Starlin Castro and Cincinnati's Joey Votto.
Ibanez was at DH Sunday to prevent him from playing five straight days in the field.
"I'm just trying to keep them from also getting hurt," Girardi said. "One of the biggest reasons guys get hurt is because of fatigue. You have to be careful."