Sources told ESPN that Gordon failed a drug test months ago, this time for marijuana.
Gordon's agent, Drew Rosenhaus, didn't comment to ESPN except to say that the information from their report was "not true."
Last season, Gordon was suspended the first two games without pay and was fined two additional game checks for violating the NFL's Policy and Program for Substances of Abuse. Despite missing time, he was the top receiver for the Browns as he caught 87 passes for 1,646 yards with nine touchdowns.
For the 2014 season, he was expected to be the top target for either Brian Hoyer or Heisman Trophy winner Johnny Manziel, who was drafted in the first round on Thursday.
Gordon did fail a drug test for using marijuana while a collegian at Baylor in 2011, which led to his dismissal from the Bears' program. He transferred to Utah as a result but never played for the Utes, then declared for the supplemental draft and was taken by Cleveland in the second round.