A decision on whether Murray will play his first game since spraining his left ankle Oct. 28 will be made after he goes through a workout before Sunday's game against the Seattle Seahawks.
"He definitely progressed," Kingsbury said. "So we want to make sure that he's in a place where he can play his game, protect himself and do all the things, and if he can, he'll be out there."
The message from the Cardinals has largely gone unchanged in the past few weeks, and Murray has gone through pregame testing the past couple of games before being listed as inactive. However, Kingsbury said he was more hopeful this week about Murray, who returned to practice in a limited fashion Wednesday and Thursday and was on the field for the open portion of Friday's practice.
The coach said the Cardinals will have a better gauge of how Murray is feeling over the next two days as he continues to rehab.
Murray is still limited by "the acceleration stuff that really makes him who he is at times" but is "getting close," Kingsbury said.
"He's got to be able to use that to get away, escape trouble, the things that he does naturally and instinctively," the coach said. "So we're still trying to get to that point."
The risk of Murray returning too soon, Kingsbury said, is reinjuring his left ankle.
"If he can't get away like he's used to doing, then you don't want to put him in harm's way where that thing can get rolled up again," the coach said.
If Murray doesn't play Sunday in Seattle, the NFC West-leading Cardinals (8-2) might face a decision on their starting quarterback. Backup Colt McCoy injured a pec Sunday against the Carolina Panthers and is "getting there," Kingsbury said.
Arizona will be without wide receiver DeAndre Hopkins for a third straight game Sunday, the coach said. Hopkins suffered a hamstring injury in the first half of Arizona's loss to the Green Bay Packers on Oct. 28 and hasn't played since. Kingsbury said he expects Hopkins to return after Arizona's bye next week.