Gutierrez, 29, has been sidelined for 24 days since being struck on the side of the head by a pickoff throw to first from Boston's Franklin Morales on June 29. Gutierrez's attempted return was slowed by ongoing headaches last week while he was taking batting practice and working out with the club on its road trip.
Wedge said Gutierrez hasn't had any headaches for several days.
"All the tests were negative, which is a big deal, both personally and professionally," Wedge said. "He's going to start getting back to exercising and doing some things physical today. Obviously, the next step beyond that is to get back into baseball activity. He's had a couple, three days with no headaches. That's a good sign. We'll see how he does now with activity."
Gutierrez has played just 13 games this season, having missed the first two months of the year with a partially torn right pectoral muscle that occurred early in Spring Training.