Rapoport reported on Twitter that a possible failed test stemmed from supplements Irving was taking and even marketing.
There is scuttlebutt Irving's appeal will center around how he came to have the supplement, but whether that impacts the NFL's decision is up in the air.
Mike Fisher of 105.3 The Fan was the first to report the news, and Bleacher Report's Jason Cole later confirmed.
"I'm told the result of the test is not yet "official" and that an appeal can be expected", wrote Fisher on Tuesday morning.
The Dallas Cowboys defense may be a bit depleted when the 2017 season starts, as defensive end David Irving is facing a four-game suspension. He led the Cowboys with 26 quarterback pressures and added four sacks.
He is now playing under a one-year tender as an exclusive-rights free agent. He's set to become a restricted free agent after 2017. He joined the Cowboys early in the 2015 season off the Kansas City Chiefs' practice squad.
The former Iowa State standout initially produced 13 total tackles, 0.5 sacks and one pass defense as a rookie.
If he is found to have violated the league's PED policy, then the Cowboys will more than likely look at their first-round pick, Taco Charlton, to fill in for Irving.