Brian Hoyer did not practice on Wednesday.
"It's in the questionable category," head coach Bill O'Brien said. "And he would have to practice to play."
The Texans quarterback remains in the concussion protocol, after he left Monday night's win late in the third quarter. T.J. Yates quarterbacked the offense for the remainder of the third and all of the fourth quarter.
O'Brien also said that Hoyer would need just one practice to be able to play. Zac Dysert, who is on the practice squad, would back up Yates on Sunday if Hoyer were unable to go.
Hoyer has thrown 13 touchdowns and four interceptions this season, and completed 59.5 percent of his passes for 1,704 yards.
The Texans will practice at the Houston Methodist Training Center on Thursday and Friday, and host the Jets on Sunday at NRG Stadium.