Happ, who is one or two starts away from rejoining the big league club, pitched four innings in a rain-shortened game with Triple-A Buffalo on Tuesday, allowing only a single earned run on three hits and two walks, while striking out three.
However, his right knee still isn't fully healed.
"When he moves off the mound, it's still not 100 hundred percent," general manager Alex Anthopoulos said. "Obviously he can go out there and pitch, but it's still a little stiff at times."
Santos pitched a scoreless inning on Tuesday with Buffalo, and was scheduled for another inning on Wednesday, marking his first back-to-back appearances since having bone spurs removed from his right elbow.
The trio of Luis Perez, Kyle Drabek and Drew Hutchinson, who have all undergone Tommy John surgery in the past year, are all pitching and nearing a return.
Drabek has made five starts with Class A Dunedin, and is close to moving up to Double-A New Hampshire.
"The last two or three have been very good, command's been good. He's been 92-94 [mph]," Anthopoulos said. "Maybe an outing or two more we'll get him up to New Hampshire. We're watching his innings just coming off of the second Tommy John."
Hutchinson, also in Dunedin, has only made two appearances, one of them starting, and the club is looking for his command to improve before making any decisions regarding him.
He has only pitched a high of 2 2/3 innings, and has averaged more than a walk per inning.
Perez is expected to start a rehab in early August, and is expected to be among those called up in September, if not sooner.