If he is suspended for any part of the coming season, it will be Irving's third suspension in three seasons.
Earlier Tuesday, Dallas defensive end Randy Gregory was suspended indefinitely for violating the NFL's Policy and Program for Substances of Abuse and the terms of his conditional reinstatement.
Irving will be a free agent when the league year begins in March, and the Cowboys have not given any indication that they are planning to bring him back.
Irving is coming off his second straight year in which he was suspended for the start of the season for a violation of the NFL's drug policy.
Now, he is expected to spend part of this offseason trying to fend off, or limit, another potential suspension for violations of league policies, sources said.
Just this week, Irving posted a message on Instagram, explaining why he is in the NFL.
"I'm in the NFl [sic] because I'm great at what I do," Irving wrote. "I'm not in the NFL because I'm an Eagle Scout, or the perfect model citizen. I didn't put on a mask or kiss ass to be where I am. I'm here on natural ability. This is God's plan. Not mine. Trust me, I'm adjusting to it as well. Once I step on the field and stop performing, THEN we have a problem ... So does anyone have anything to say about my play?"