Girardi said that Cooper will see some reps at first base, though Chase Headley remains the everyday first baseman. If Cooper plays, it will likely be against a left-handed starter.
"I'll incorporate Coop a little bit," Girardi said. "With Head, I'll give him a day off here and there. If it comes, it'll come against a lefty."
Holliday is batting .229 with 16 homers and 51 RBIs in 88 games this season, his first with the Yankees. Girardi said that he is hopeful Holliday can return in the minimum 10 days.
"I hope that's all it is," Girardi said. "Backs are tricky, so you've got treatment, and do what you've got to do."
In Holliday's absence, Girardi said that he sees several different ways that the Yankees could spread around at-bats in the DH spot. Gary Sanchez could take additional reps there, with Austin Romine catching, or the at-bats could be doled out among the club's four outfielders.
Aaron Hicks is rehabbing from a right oblique strain at Triple-A Scranton/Wilkes-Barre, but Girardi indicated that it is unlikely Hicks will join the Yankees for the upcoming series against the Blue Jays in Toronto.
"I think the tricky part there is the switch-hitting," Girardi said. "If he wasn't a switch-hitter, you could probably speed it up."
Bryan Hoch has covered the Yankees for MLB.com since 2007. Follow him on Twitter @bryanhoch and on Facebook. This story was not subject to the approval of Major League Baseball or its clubs.