Stanton went on the disabled list on April 30 with a strained right hamstring. He has done some hitting in the cages and is playing catch.
"I'm hitting and throwing," Stanton said. "That's good that I can do that."
But as for running, Stanton has progressed from doing jogging in a therapeutic pool to running on a special anti-gravity treadmill, which he has done the past two days.
Stanton is recovering from a Grade 2 hamstring strain, which roughly takes four to six weeks from which to recover.
"I don't know how long it's going to take," Stanton said. "Once I can do normal jogging and running, it will be better to figure that out."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter