On his Twitter page, the right-hander wrote on Thursday: "Update for everyone! Bullpen tomorrow, 1 step closer!! Thank u for all the support!!"
Chamberlain previously had thrown off a half-height mound to help regain his form since he was hurt bouncing on a trampoline with his son on March 22.
Yankees manager Joe Girardi said he didn't know about Chamberlain's plans. Chamberlain is at the Yankees' minor-league complex in Tampa, Fla.
"That, I'm not aware of," Girardi said Thursday.