After that, the team will address the next move for Putz, who was 2-1 with five saves in nine chances this season with an ERA of 4.26.
"Hopefully he'll be ready to go somewhere. Wherever that might be," Gibson said.
Hill is now off to Triple-A Reno to continue his rehab. He's expected to play Saturday and Sunday, take Monday off, and if everything goes well, play again Tuesday and Wednesday.
Hill has been on the disabled list since April 15 with a slight fracture in his left hand and was hitting .306 with two home runs and six RBIs in 10 games.
"It'd be good to get those guys healthy," Gibson said. "It gives us some options."
Jamal Collier is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.