Mijares threw a light session off the mound on Tuesday, and will throw in the bullpen on Wednesday.
"If that goes well, he'll go out on a rehab assignment somewhere this weekend," McWane said.
McWane added that Perkins is still making good progress with his strained right oblique.
Slowey, whose MRI on his oblique and abdomen came back negative on Monday, will see a doctor on Wednesday morning to check for a possible hernia.
Twins manager Ron Gardenhire was asked if he was expecting to make a move with Slowey going somewhere after Tuesday's game. Still unsure if Slowey had any sort of injury, Gardenhire indicated the decision would not come until after Slowey's visit to the doctor.
"I'm still waiting to see what we have," Gardenhire said. "He's going to see a hernia doctor, we're going to see if there's any issues there, and if that's clear, then we'll probably do something."