Each day, Kubiak grows more concerned about Davis' lack of availability during a week in which the roster will be reduced to a final 53 on Friday, one day after the Texans close preseason at home against Tampa Bay.
"I'm very concerned," Kubiak said. "There's not much we can do about it, but I'm very concerned about that situation. It'll be a tough decision for the final 53. We'll make the decision based on what's best for Domanick and the team."
The Texans will have several options. They can make Davis part of the final roster and wait for him to get healthy. They can place him on waivers. They can put him on injured reserve, which means he wouldn't play this season. They also could trade him, which is unlikely because he's damaged goods.
Davis can't be placed on the physically unable to perform list because he passed the team's physical before training camp.
Asked what has to happen for Davis to be on the 53-man roster, Kubiak said, "We have to see something that shows he's making a lot of progress.
"Before the game Thursday, we'll probably have a sit-down with Domanick, the doctors, possibly his agent and everybody involved in the process to see where he is. That's going to be a big call.
"The farther we go without him being on the field, the tougher that decision becomes. And when I say tough, it doesn't necessarily mean that Domanick won't be on the 53-man roster. If he's definitely making progress, and everybody thinks he's going to be able to play, then he will be (on the final roster)."
Davis, who turns 26 in October, was on his way to a third consecutive 1,000-yard season a year ago but came up 24 yards short because of the knee injury. The surgery removed part of his lateral meniscus.