After Monday's game, he said he's still feeling some soreness in that area, but he plans on playing catch again on Wednesday to determine if he'll be able to throw a bullpen session in anticipation of a possible start on Sunday in Kansas City.
"He definitely still feels it in his arm," manager Ron Gardenhire said. "It's better but not gone."
Slowey had been on strict orders from the training staff to rest the arm and do nothing but stretching exercises since the injury.
"It feels better now than it did when I hurt it," Slowey said. "I at least know that I'm progressing. Whether I'm 100 percent right now or I'll be 100 percent in a day or two, we'll see.
"Being an athlete, you want to go out and do your job," Slowey added. "For me, just going out and being able to throw, that's an everyday occurrence for me. It's kind of tough. Our trainers are great. They were pretty emphatic about giving it a couple days to calm down."
"We have to get a feel where he's at," Gardenhire said. "He's got to be able to do a bullpen session -- probably one or two of them."
Francisco Liriano, who is making his second Minor League start on Tuesday, would also be on track to start Sunday depending on how he fares for Rochester. If Slowey and Liriano are ready to go this weekend, there will be a decision to make in the rotation -- but Gardenhire isn't worrying about that just yet.
"First, we've got to see how [Liriano] does," Gardenhire said. "Then we'll make a decision on what we'll do. He should be stretched out to pretty close to 100 pitches tomorrow. Then we'll make a decision after the ballgame as to what we're going to do next. If it goes good, bring him up here."
Kerry Walls is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.