Perkins, who allowed three runs without recording an out on Sunday, stayed back in Minnesota to undergo an MRI exam on his forearm on Monday, which showed only inflammation in his left forearm.
"Perkins is doing better," Twins general manager Terry Ryan said. "It's going to be an early-morning decision on whether he flies and joins us."
Perkins, though, remains a candidate to be placed on the disabled list if he's not ready to go, as the Twins plan to recall right-hander Jason Marquis from Double-A New Britain to start Wednesday's game against the Yankees.
Another candidate to be placed on the disabled list is right-hander Nick Blackburn, who is missing his scheduled start on Thursday because of stiffness in his right shoulder. Blackburn is slated to throw bullpens on Friday and Sunday with the hope of returning to the rotation on Tuesday.