Twins head trainer Rick McWane said Baker "felt great" throwing long toss on Tuesday.
"After he throws his bullpen, we'll make a decision on if he needs to go on a rehab," McWane said.
Right-hander Kevin Slowey (abdominal strain) is scheduled for another rehab start on Wednesday in Rochester, with no pitch limit.
Outfielders Jason Kubel and Denard Span continued to rehab at Triple-A as well, with both scheduled to start on Tuesday night. Kubel was set to DH for nine innings, while Span was expected to play seven innings in center field.
Through two rehab games entering Tuesday, Kubel was hitting 1-for-8 with a double and four strikeouts, while Span was 0-for-6 with a strikeout.