Cushing fell ill during a team meeting on Tuesday night. He remained in the hospital as of Wednesday afternoon.
"He's doing better," Kubiak said Wednesday afternoon, via the Texans' team site. "All his tests came back good."
Kubiak hopes he can have his star linebacker back at practice on Thursday.
"I would hope so," he said, via the Houston Chronicle. "We're not going to do a whole lot in the morning. We're going to come out in shorts, and we're just kind of preparing for Carolina now, freshen them back up until Saturday. If Brian's feeling good, I'd like to see him get his work in. As you can tell, I think he's going to be fine. If he misses tomorrow, then we'll have to reevaluate where we're at."