Murray returned to practice Friday after missing five straight. He last practiced the week of Arizona's Thursday night loss to the Green Bay Packers, against whom he sprained his left ankle late in the fourth quarter.
"He's progressing," Kingsbury said. "Obviously, it's good to have him out there. See how he feels tomorrow and Sunday and go from there."
Murray doesn't have to be "100 percent" healthy to play Sunday against the Carolina Panthers, Kingsbury said. He wants to make sure Murray can "move well enough to protect himself."
"He's got to be able to move enough to where he can protect himself, do what he does, escape, extend plays, things of that nature," Kingsbury said.
Murray felt like had made "crazy strides" from a week ago, he said Wednesday. He missed the first game of his NFL career on Sunday against the San Francisco 49ers. In his place, backup quarterback Colt McCoy led Arizona to a 31-17 win.
The Cardinals have discussed "all possibilities" relating to their approach to Murray and whether to rest him for another game or play him Sunday if he's ready.
"I mean, in this league, it's week-to-week, as you know," Kingsbury said. "You got to try to win every game you have an opportunity to win. So, if he is ready to go, he'll play."
Kingsbury said Murray is "not that fun to be around currently" because of how much he wants to play Sunday.
Kingsbury also said wide receiver DeAndre Hopkins will be a game-time decision with a hamstring injury. He's hopeful Hopkins will be ready to play after missing the third game of his career on Sunday, but said he wasn't sure.
"You don't want to lose somebody like that for an extended period of time, if you can help it, and he hadn't missed many games in his career," Kingsbury said. "So, we want to make sure when he's back, he 100 percent can do everything he does."
Kingsbury expects safety Budda Baker to play against the Panthers after being on the injury report with a concussion and knee injuries throughout the week. Kingsbury was also hopeful that wide receiver Rondale Moore will play Sunday with a concussion and a neck injury.