Montero was set to catch three to five innings Monday, take Tuesday off and catch around five innings on Wednesday. Arizona is hopeful that Montero can catch a full game by Saturday.
"We'll see how he's playing, how he's feeling, how he's swinging," D-backs manager Kirk Gibson said.
If all goes well, Montero might be able to join Triple-A Reno next week while it is in Tucson.
Reno might get an influx of players that week if infielders Eric Chavez (knee/hip) and Willie Bloomquist (hand) are ready to begin their rehab assignments.
Speaking of injuries, Gibson said there's a chance that left-hander Matt Reynolds (elbow) could rejoin the team before the end of the season.
Reynolds, who has been out since June 10, has not yet thrown off a mound, but is throwing from a distance of 100 feet.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.