Gordon, who is facing a yearlong ban after a failed drug test earlier this offseason, will file the appeal in New York, the source told Schefter.
Gordon, 23, spent two weeks in rehab in California after he was subsequently arrested and charged with driving while intoxicated and speeding in Raleigh, N.C., earlier this month, a source confirmed to Schefter on Thursday.
Fox Sports earlier reported Gordon's rehab stint.
The Browns open their training camp on Saturday, meaning they will have at least one more week of uncertainty regarding the status of the talented but troubled Gordon.
ESPN's "Outside the Lines" reported in May that Gordon was facing the suspension after failing the drug test months prior.
Gordon ran into more off-the-field trouble when he was arrested and charged with the DWI.
Browns first-year coach Mike Pettine acknowledged earlier this week that Gordon's situation is "concerning" but said that Cleveland still was awaiting the NFL's ruling.
"It is concerning and you want to address it, but until we know where he stands with the league we don't know really where he stands with us," Pettine said Monday. "I've stated before that we've had the meetings, we've discussed all the options, from the best case to the worst case. And we're still in that mode of waiting."
Gordon had 87 catches for 1,646 yards last season and became the first player in NFL history to have consecutive 200-yard-receiving games.
ESPN.com Browns reporter Pat McManamon and The Associated Press contributed to this report.