Gordon is facing a year-long suspension after allegedly testing positive for marijuana, according to ESPN.
ESPN also reported Gordon's agent, Drew Rosenhaus, didn't formally comment but denied the report.
He faced problems in college after having failed three drug tests - two at Baylor and one at Utah without even having played a game.
Gordon served a two-game suspension for allegedly testing positive on a test last offseason.
With as deep as this year's receiving group is, it begs the question whether the Browns would have traded a third round pick - the third round pick they acquired last year from Pittsburgh in a draft-day trade - as part of a package to move up and take quarterback Johnny Manziel.