Bradley, who was placed on the 15-day disabled list because of right shoulder tendinitis June 4, threw a bullpen session Monday and last Friday. He'll need at least one rehab start in the Minor Leagues before the club considers bringing him back.
"I think that was the plan, a rehab start or maybe two, just depending on where I'm at pitch-wise and all that," said Bradley, who is eligible to come off of the DL on Friday. "We'll know a lot more [Wednesday] after the sim-game. Sim-game [on Wednesday] and take it day by day from there."
Bradley went 1-0 with a 1.80 ERA in four April starts. He landed on the disabled list April 29 after being hit in the face by a line drive off the bat of Rockies outfielder Carlos Gonzalez. The right-hander went 0-3 with a 10.91 ERA in four outings after returning to the rotation May 16.
"Feels good. Feels like it is getting back to where it was at the beginning of the year," Bradley said. "I feel a lot stronger and I'm ready to get back going again."
It's unclear if the D-backs will have room for Bradley in the big leagues when he is cleared. Arizona pitchers are 4-1 with a 1.23 ERA and a .174 opponents' average in their last five games, a span of 44 innings.
"He felt great. The reports on his last couple of outings -- the side-work -- have been really good," manager Chip Hale said. "He's starting to feel like he did at that start of the year. That's a positive."
Jesse Sanchez is a national reporter for MLB.com. Follow him on Twitter @JesseSanchezMLB. This story was not subject to the approval of Major League Baseball or its clubs.