Thome, sidelined since June 2 with a strained left quadriceps, has made progress over the weekend since receiving an epidural on Friday. Before the Twins' series finale with the Rangers on Sunday, Thome even took some swings in the cage.
"I'm feeling good," Thome said. "I swung and had no issues today. Everything went good."
Manager Ron Gardenhire said before Sunday's game that if everything went well, the club would send Thome to Florida.
"He said he would really like to get to Florida and start getting in that heat and start doing his rehab down there and get back to swinging," Gardenhire said. "He likes that program down there because it's controlled pretty well, but he can get a lot of work in because there are so many bodies down there that are willing to try to do something."
Until he begins working in Fort Myers, though, Thome won't know whether he'll be ready to return to the Twins when he becomes eligible on Thursday.
Even if it takes Thome a few extra days to return, the Twins should have a pretty formidable lineup when he does, with Joe Mauer and Tsuyoshi Nishioka expected back from the 60-day DL in the next week.
"I think it's exciting, yeah," Thome said. "Especially with as hard as those guys have worked down there, Nishi and Joe, and the rest of the guys here obviously have done a great job lately. So it's kind of exciting to see where our team could go."