Parnell, 29, arrived at the Mets' spring training complex in Port St. Lucie, Fla., this week to ramp up activities under the supervision of team personnel. That is well ahead of the official Feb. 15 report date for pitchers and catchers.
Parnell was examined in California in late December by Dr. Robert Watkins, the surgeon who performed the closer's procedure. Parnell was fully cleared for baseball activities during that examination.
"I've been throwing for several weeks now, taking it nice and easy," Parnell said. "… I'm getting into the baseball activities slowly, and with some professional eyes on me.
"From talking to the surgeon, he's given me the full release for baseball activities. He said, 'Just take your time getting ready and be smart about it.' That's why I came to Florida early -- to have the eyes on me, to make sure we're doing it the right way, to be smart about it."
Parnell, who converted 22 of 26 save chances last season before being shut down for the season on July 30, is expected to return to the closer's role. In reality, the Mets do not currently have viable alternatives, with the possible exception of right-handed reliever Vic Black.
"In my head I feel like I'm still the closer," Parnell said. "I'll go along with that until told otherwise. I feel healthy."
Parnell said he hasn't been able to do any offseason weight training while recovering.
"Obviously, I haven't been able to lift weights like I would have in years' past," Parnell said. "I can't get under a squat bar, obviously, so I have to be creative in the way that I work my legs. Running -- the impact, early -- might aggravate it. I have to slowly progress into that.
"The last two months I would have been in the weight room several times a week and would have been a little bit in better shape coming down here. But with the injury and everything, I knew that it was a possibility I wouldn't be in the shape I would have liked to have been coming into spring training. So that's why I'm here early."
Parnell said team officials' reports that he lost as much as 30 pounds were overstated. He said he never got lower than 195 pounds and is now back up to his normal weight of 207-208 pounds.
Parnell, one of four arbitration-eligible Mets whose 2014 salary remains unsettled, is projected to earn $3.725 million. Second baseman Daniel Murphy, right-hander Dillon Gee and first baseman Lucas Duda also have not settled.
Shortstop Ruben Tejada agreed on a one-year, $1.1 million deal Wednesday. First baseman Ike Davis agreed Thursday to a $3.5 million, one-year contract. Left fielder Eric Young Jr. has a $1.85 million, one-year deal set to be announced Friday.
The Associated Press contributed to this report.