Melvin said he will get daily updates from the training staff regarding the process for Reddick going forward.
Reddick's DL stint is retroactive to June 1, meaning he is eligible to be activated for Monday's series opener against the Rangers. But Melvin said Reddick could be well-served to take a short rehab assignment.
"I think, to an extent, it might do somebody some good just to see some live pitching," said Melvin. "Maybe not a real long one, but he's been out long enough where probably a game or two wouldn't hurt him. But I don't know for sure yet."
Reddick hurt his knee banging into the wall while making a catch against the Angels on May 31.
He is hitting .214 with four home runs and 22 RBIs in 168 at-bats.
Aaron Leibowitz is an associate reporter for MLB.com.