Drew said Sunday that he had an MRI after the season and the exam didn't show any serious damage. He said he fought the injury all offseason, but it continues to linger.
"It's still pretty stiff," he said. "I've been able to hit and run and all of that stuff. I'm just in the maintenance stages."
Drew was limited to 109 games last season, batting .280 with 19 home runs and 64 RBIs. He was the MVP of the All-Star Game at Yankee Stadium after hitting a tying homer.
The 33-year-old outfielder said he could play right now if the team needed him.
"The herniated disk seems to be the major cause of the stiffness and irritation," he said. "As long as you can keep that from being too inflamed, I guess you'll keep the back, as far as playing shape goes, in good shape. Everything is well enough to perform and play."
Drew arrived in camp several days before position players are due to report to meet with the team's medical staff and work out under the club's supervision.
"I'm hopeful," Drew said. "You can only do so much. I'm very, very hopeful that the program we have will work. My body will tell me. I know right now it's stiff and I can play."
Drew played in just two regular-season games after Aug. 17 before playing in 10 of Boston's 11 postseason games. His biggest moment came in Game 5 of the AL Championship Series when he drove in three runs, including the game-winner, to help Boston erase a 7-0 deficit and beat Tampa Bay 8-7.
"I actually played way better than I ever expected and had some huge hits in the series against the Angels and then against Tampa," he said.