Blackburn, who has an 8.37 ERA in eight starts, was placed on the disabled list on May 17 with a left quad strain. He's scheduled to throw a bullpen on Saturday.
"We're looking at Blackburn maybe going down to rehab to get a couple of starts," Gardenhire said. "Probably in Triple-A, but it depends on the best situation for him. But that's in the works. It hasn't been decided yet. We have to get him healthy."
Reliever Kyle Waldrop is also slated to start another rehab assignment with Class A Fort Myers on Saturday, as he returned to the Twin Cities this week to undergo a precautionary MRI exam on his right elbow.
Waldrop, who is on the disabled list retroactive to March 26 with a strained right elbow, made two scoreless appearances with Fort Myers before dealing with soreness in his elbow.
"I got another look on Monday just to be safe, but it's fine," Waldrop said. "I threw a bullpen today to maintain and then I'll be back with the Miracle tomorrow. So I'll get a couple more games to get ready."
Fellow reliever Alex Burnett felt some discomfort in his right elbow after his one-inning stint against the White Sox on Wednesday, but said he's feeling better.
Burnett said he should be ready to pitch again on Saturday and doesn't think he'll need a stint on the disabled list.
"It's good," Burnett said. "It's more like a stinger, basically. But it feels good, and hopefully everything should be good."