"It's getting there, and he's really, really close," Braves manager Fredi Gonzalez said.
Simmons has been sidelined since jamming his right shoulder during Monday's win over the Marlins. The dazzling young shortstop has played just six games since missing two months with a fractured fifth metacarpal in his right hand. He was also hobbled last week by a sprained right ankle.
The Braves will be without backup shortstop Paul Janish for the remainder of the regular season and possibly through the first couple weeks of October. Janish dislocated his left shoulder while diving to his right during Tuesday's loss to the Marlins.