Thole, who has been on the disabled list since May 8 with a concussion, will begin baseball activities this week at the team's Spring Training complex in Port St. Lucie, Fla. He could appear behind the plate in a Minor League game by early next week.
"He's accomplished all of the running and the biking to get the blood pressure to see if there's any headaches," manager Terry Collins said. "There's none. So now we'll start the next stage."
Bay also left for Florida on Monday after testing his fractured left rib with soft-toss swings in Toronto and Pittsburgh. Bay will take regular batting practice for the first time Wednesday, putting him on track for a return around the end of the month.
Shortstop Ruben Tejada, who has been on the DL since May 7 with a right quad strain, has already been in Florida for more than a week. Tejada increased his running program Monday and, barring any setbacks, could rejoin the Mets as soon as this weekend.