In previous years, the Cowboys have used the third quarterback to play in the final preseason game, which was the case with Stephen McGee and Richard Bartel. The No. 2 quarterback was made available in case of injury.
This summer, Tanney has completed 54.8 percent of his passes with one touchdown and one interception for 246 yards.
The opportunity to keep three quarterbacks on the roster is remote given how the Cowboys are trying to keep four running backs, four tight ends, make room for an extra safety and defensive lineman.
But Stephen Jones, the Cowboys executive vice president, left the door open about keeping a third quarterback.
"Those are things you always look at on merit and a full body of work and you look at what it means to other players in terms of who we could keep and how they could contribute," Jones said. "As I said, that decision still is yet to be made. The bottom part of the roster, how they play and what they do and how they perform against the Texans is going to have some influence. It’s a full body of work still."