Swisher hit in the batting cages on Thursday and will get on the field during batting practice Friday. Gardner is scheduled to hit in the batting cages on Friday and take live batting practice on Saturday, testing his strained right elbow.
"[I feel it] a little bit in my follow-through," said Gardner, who is eligible to be activated from the disabled list. "Hopefully it'll be better and I don't have any setbacks, so I'll be good to go."
Yankees manager Joe Girardi said that Gardner would probably need at least one Minor League rehab game, essentially ruling out that he could play this weekend against the Royals.
Girardi did not know if Swisher -- who is not on the disabled list with left leg pain -- would be available to play before Tuesday against the Rays at Yankee Stadium.
"I don't know. We'll see," Girardi said. "Let's see how the next couple of days go."