"Everything is going in a very good direction and is trending in a positive way," Lovullo said. "We're very happy."
Ray was taken to the hospital and had two staples put in the side of his head to close a wound in addition to being diagnosed with a concussion. He returned to Phoenix before the team went to San Francisco and was cleared for baseball activities Thursday.
Ray played catch Friday and Saturday, extending out to as much as 125 feet away, before getting a day off Sunday. While the team's excited with his progress so far, Lovullo said it's unlikely Ray returns when his spot in the rotation comes up Thursday against the Dodgers.
"What the plan is beyond tomorrow, I don't exactly know," Lovullo said before Sunday's series finale vs. the Giants. "We want to get him through the first bullpen and then come up with a game plan."
Rookie Anthony Banda, the team's No. 4 prospect according to MLB Pipeline, gave up one run in six innings Friday in Ray's rotation spot. But the team said the starter for Thursday is still to be announced even as Banda stays with the team. With Monday's day off, the team could elect to skip Ray's spot and have right-hander Taijuan Walker pitch on his normal rest.
• Randall Delgado (flexor strain in right elbow) played catch from 90 feet out Saturday as part of his throwing program, but Lovullo said the team doesn't yet know when he'll get back on a mound.
Alex Simon is a reporter for MLB.com and covered the D-backs on Sunday. Follow him on Twitter at @alexsimon99. This story was not subject to the approval of Major League Baseball or its clubs.