"He's been great since he's been over here," D-backs manager Kirk Gibson said.
Gibson was then asked about whether Ziegler might fill that role next year.
Putz and Bell are both under contract for next year while Ziegler is eligible for salary arbitration. His time and success this year in the closer's role will likely mean he will earn more money through the arbitration process.
"I don't know that we're there yet," Gibson said about next year's closer. "I hope he wins about 15 games for us next year. We're just trying to get through this year and play it out like we should. And then they all turn into businessmen and a different phase of our season starts."
Last month, Putz praised the job that Ziegler has done and talked about how he understood why Ziegler would fill the role for the rest of the season.
The veteran then broke into a smile.
"But I'm going to take it back from him next year, I'll tell you that right now," he said.
Steve Gilbert is a reporter for MLB.com. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.