Feliciano was advised to begin a six-week shoulder strengthening program on Monday, visiting Dr. James Andrews in Pensacola, Fla.
The 34-year-old left-hander has a capsule tear in his pitching shoulder, and going under the knife would put him out for at least all of the 2011 campaign.
"He's going to try to rehab it and we'll see if we can use him at some point this year," manager Joe Girardi said. "Sometimes players like to do that. Players don't want to miss full years. It's hard to take."
Girardi said that Feliciano will join the team after their five-game trip to Toronto and Baltimore and perform his rehab in New York.
Capsule tears can be a difficult injury to return from; former Yankees right-hander Chien-Ming Wang has still not pitched in a Major League game after suffering a similar injury in 2009.
"I think there's a risk in the surgery as well," Girardi said. "The injury that [Feliciano] has, there's no guarantees that the surgery is necessarily going to fix it by the end of next year anyway. It's kind of the game that you play."