The Cowboys hired Linehan to take over play-calling duties from offensive coordinator Bill Callahan in the offseason. Linehan spent the last five seasons as the offensive coordinator for the Detroit Lions.
Jones said Romo will be an "improved player" with Linehan handling the play-calling.
Romo, 34, is returning from back surgery. He played in two preseason games and completed 14 of 23 passes for 167 yards, one touchdown and zero interceptions.
"You're not going to see a distraction," Jones said about Bryant.
The Cowboys open the regular season Sunday when they host the San Francisco 49ers.
- Paul Palladino