The receiver may appeal, but it's unlikely to work, Rapoport added.
"Clearly we are very disappointed to hear the latest report regarding Josh," the team said in a statement. "At this point, due to the confidential nature of the NFL's substance abuse policy, we have not been made aware by the league of a failed test. We are in the process of gathering more information and will provide further comment at the appropriate time."
The banishment comes on the heels of a bizarre 2014 season, in which Gordon missed the first 10 games of the 2014 season after violating the league's substance-abuse policy. The wide receiver was reinstated and played in five games before being suspended by the Browns for the final game of the season for violating team rules.
Gordon was also suspended for two games in 2013 for violating the league's substance-abuse policy. Following the ban, the wideout had a breakout season, leading the league in receiving.
After returning from his 10-game suspension in 2014, Gordon compiled 24 receptions for 303 yards in five games.
Per NFL rules, Gordon's contract now "tolls," meaning he is under the Browns' control through 2016, after which he will become a restricted free agent, Rapoport added. Had Gordon not been suspended for the final game of 2014, he would be an unrestricted free agent after 2015.
With the latest news, he'll likely have to wait until 2016 to take the field.