Morneau underwent neck surgery on June 29 to repair a pinched nerve, and is expected to be out until at least mid-August.
"He's been working out, doing some cardio," McWane said. "He can do pretty much what he wants to in the weight room and off the field. But he's not going to throw and swing for about another week or so."
McWane also gave updates on several other injured Twins.
Kevin Slowey (abdominal strain) is scheduled to start on Friday for Triple-A Rochester. McWane said he expected Slowey to be limited to about 90 pitches.
Scott Baker, who skipped his last start due to a right elbow strain, is scheduled for a bullpen session on Friday afternoon.
"His elbow feels a lot better," McWane said. "We anticipate him making a start on Monday."
Thome has been battling a sprained toe on his left foot, and was a late scratch on Thursday afternoon.
McWane said Thome felt better, but wanted to run around and test it out before returning to the lineup. Thome was available to pinch-hit against the Royals.