Dallas Cowboys quarterback Ben Dinucci. Kirby Lee-USA TODAY Sports

Ben DiNucci will not be on the Cowboys’ 53-man roster to start the season. Dallas is cutting the third-year passer, Todd Archer of ESPN.com tweets.

The former seventh-round pick was behind Cooper Rush and Will Grier on the Dak Prescott-topped depth chart. Rush and Grier have vied for the backup job during the preseason, and the presence of both could impact DiNucci’s status as a practice squad arm.

That said, the Cowboys kept three quarterbacks last season, with Rush — who returned after his Giants stint — and Grier on the team’s active roster. DiNucci, who started a game and played in three during Prescott’s injury hiatus in 2020, spent last season on Dallas’ P-squad. DiNucci, who attempted 43 passes as a rookie out of James Madison two years ago, stayed with the team via reserve/futures contract this offseason.

Teams must pare their rosters from 80 to 53 by 3 p.m. Tuesday. Waiver claims will process Wednesday afternoon. At that point, teams can begin assembling their practice squads. Despite the NFL doing away with the reserve/COVID-19 list this season, taxi squads remain at 16 players. If the Cowboys are planning to keep the same arrangement as 2021, DiNucci — should he clear waivers — would be on track to stick with the organization as its fourth QB.

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