The right-hander was promoted to Triple-A Reno last month, and he's gone 2-0 with a 2.52 ERA in his first four starts for the Aces.
With Ian Kennedy, Daniel Hudson, Joe Saunders, Trevor Cahill and Wade Miley pitching well, the D-backs do not have a spot for Bauer.
D-backs GM Kevin Towers was asked Wednesday if the organization was looking to try to make room for Bauer.
"Not really," Towers said. "Those things kind of work themselves out."
It is possible the D-backs could choose to deal Saunders, who will be a free agent at season's end, or an injury could open the door. Until something changes, though, Bauer just has to be patient.
In 12 starts between Double-A Mobile and Reno, Bauer, who was the No. 3 overall pick in last year's Draft, has compiled a 9-1 record to go with a 1.96 ERA.
"He's pretty much done all he probably can do at Double-A and Triple-A, and he's been very successful at it," Towers said. "Sometimes you just have to wait your turn -- you know wait, for that opportunity.
"How that opportunity presents itself -- be it an injury or a trade or somebody's not performing and ends up going down and then you take advantage of it. But right now, I don't know who I'd take out of the rotation to make room for him, and I don't want to put him in the bullpen."
Towers also said that going with a six-man rotation was not under consideration.