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.
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, 23, ran into more off-the-field trouble earlier this month, when he was arrested and charged with DWI in North Carolina.
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.
Browns WR Gordon To Appeal Suspension
Adam Schefter has the latest on Browns WR Josh Gordon, who will appeal his one-year suspension in a meeting with NFL officials on Aug. 1.