Thayer has been on the disabled list since June 24 (retroactive to June 17) with a right shoulder strain.
Thayer had a Minor League rehabilitation outing Saturday, pitching for Double-A San Antonio, who were playing three hours away in Springfield, Mo.
Thayer started the game and allowed three earned runs on three hits, including a home run, in the Missions' 8-3 loss.
Murphy said the results weren't as important as how Thayer felt coming out of the outing.
"It was getting him out there and letting him face hitters again, that was the big thing," Murphy said. "I've been involved in a lot of those rehab assignments. You look at the numbers and things like that and throw them away. [It's] how did he feel? We know Dale, we know what he's done. The important thing is he can be ready to go."
At the time of the injury, Thayer was 2-2 with a 3.41 ERA in 29 innings.
• Catcher Derek Norris, who sprained the AC joint in his left shoulder on Friday, wasn't in the starting lineup on Sunday, though Murphy said the start off was scheduled. Norris started Saturday and caught the entire game, earning praise from Murphy with how he was able to handle starting pitcher Odrisamer Despaigne.
"He wants to play," Murphy said. "He's caught a lot, three games in a row. That AC sprain … at some point we've got to give him a day [off]."