If that goes well, Putz would then throw in back-to-back games Monday and Tuesday.
"We do want him to be able to throw back-to-back days when he comes back," D-backs manager Kirk Gibson said.
Heath Bell has filled in at closer during Putz's absence, and has saved 11 games in the interim and 12 overall.
Gibson was asked how Putz would be worked back into the bullpen mix when he returns.
"We'll get him back-to-back and see how he's feeling," Gibson said. "We're going to wait and see how he's throwing, how healthy he is, and we'll see what else is going on in our bullpen as well. I think right now our focus is on getting him healthy and making sure he's ready to pitch here."