Nathan, on the disabled list retroactive to May 24 with a right flexor muscle strain, could rejoin the Twins on Friday in Milwaukee if his outing Wednesday goes well.
Meanwhile, back in Minnesota, the injured trio of Jason Kubel (sprained left foot), Justin Morneau (sprained left wrist) and Denard Span (concussion) are showing signs of progress.
Kubel has been taking part in a running program and is starting to turn the corner with his foot sprain.
"It's getting better," Twins athletic trainer Rick McWane said. "It's still a little sore but he said it was considerably better today than it had been."
Morneau is expected to get his cast off Friday or Saturday and then will need three to seven days of rest before swinging again.
And Span is continuing to show good signs that he's feeling better based on various tests, but there is still no timetable for his return.
"He has made some progress," McWane said.