"He's passed all of his tests," D-backs general manager Kevin Towers said. "More than likely he will join us tomorrow."
Gregorius was hit in the head by a Josh Outman pitch last Friday and sustained a mild concussion.
Towers said he got a text from Minor League hitting instructor Mark Grace on Friday that said Gregorius had turned on a 96-mph fastball and had driven it to right field earlier in the day.
The D-backs will have to make a roster move when Gregorius is activated. When he was put on the DL, the team activated outfielder Jason Kubel from the regular disabled list. That means outfielder Alfredo Marte could be sent down to make room.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.