Swisher hit off a tee left-handed in the batting cages underneath Yankee Stadium on Tuesday, which he believed should be a good sign to get him back into the lineup on Wednesday against the Rays.
He had not taken a left-handed swing since leaving Friday's game after one at-bat against Minnesota's Scott Baker, as manager Joe Girardi has protected Swisher from doing further damage to the bicep.
"I'm on board with skip and the trainers," Swisher said. "I'll take [Tuesday] off, come back here [Wednesday], take BP on the field and be ready to play."
Girardi wasn't about to lock Swisher into his lineup on Wednesday against Tampa Bay, but he said it is possible the right fielder could be ready.
"I can't give you an exact date when he's going to be in," Girardi said. "Hopefully it's tomorrow. This is not something that we want to linger on."
Even though he was not in the lineup, Swisher said that he was as excited as anyone in the ninth inning on Monday, when Alex Rodriguez and Marcus Thames belted a pair of two-run homers off Boston closer Jonathan Papelbon to sink the Red Sox in an 11-9 win.
"When you're not playing and the team is winning, it's a lot easier to take," Swisher said.