Manager Manny Acta said Monday that Wood will reclaim his role in the back of the Cleveland bullpen once he's healthy enough to do so.
The 33-year-old right-hander, on the 15-day DL retroactive to July 12 with a blister on his right index finger, threw a successful bullpen session Sunday. He is slated to throw another side Tuesday, the results of which should dictate how soon he rejoins the Tribe.
"We need to see how the finger responds," Acta said. "Then we'll go from there."
Chris Perez has assumed the closer's role in Wood's absence, converting a pair of saves. The 25-year-old righty also filled in for Wood to begin the season while the veteran recovered from a strained right lat muscle.
Wood, a candidate to be moved at Saturday's non-waiver Trade Deadline, is 8-for-11 in save situations this year. Perez has nine saves in 12 opportunities.
"Whenever Kerry's ready, he'll close," Acta said. "But Chris is not going anywhere."