If Gathers makes the 53-man roster, he will miss the Sept. 8 opener vs. the New York Giants and be eligible to return to the team the next day.
Gathers was arrested and charged with possession of marijuana by Frisco, Texas, police before the start of last season. In March, Gathers reached a deal with the district attorney, reducing the charge to a Class C misdemeanor, 90 days deferred adjudication and a fine.
Gathers, a 2016 sixth-round pick, caught three passes for 45 yards last season. He is in a fight to make the 53-man roster this season and spent the offseason working as the fourth tight end behind Jason Witten, Blake Jarwin and Dalton Schultz.
He might not be the only Cowboys player to hear from the league in terms of discipline. Defensive end Tyrone Crawford was involved in an incident early in the offseason in Panama City, Florida, and Ezekiel Elliott was caught on film knocking down a security guard at an event in Las Vegas.
Neither Crawford nor Elliott was arrested, but both players are still subject to penalty via the league's personal conduct policy.