The running back is yet to practice this week, having been struggling with a hamstring injury since before the team's bye.
The head coach told reporters: "Arian went out and stretched, did some stuff and did some walk-through. And then he worked with the trainers.
"I think he's going to do everything he can to be there. But I think it'll be an end of the week decision, so we'll see. He did do some things, just not with the team once we got going.
"[Backup Ben Tate] practised, kind of like a trail run going through the week seeing how he's going to feel. But he took his normal reps with what we did [yesterday]."
The Texans face the Indianapolis Colts on Sunday.