Moore is practice squad eligible but and will likely go back to the active roster.
Rush completed 38 of 51 passes for 398 yards in the preseason with six touchdowns and no interceptions. His play earned him second-team work in practice the final two weeks of training camp.
The Cowboys are considering placing tight end Rico Gathers (concussion) on injured reserve but needed Gathers to be on the 53-man roster Saturday. Moore will not be subject to waivers and could re-sign with the Cowboys in a day.
Moore completed 32 of 59 passes for 392 yards with one touchdown and one interception in four preseason games. He missed last season because of an ankle injury suffered in training camp that led to Prescott becoming the starter once Tony Romo was hurt.
In 2015, Moore started the final two games and played in the final three, completed 61 of 104 passes for 779 yards with four touchdown passes and six interceptions.