It is unclear which NFL teams are interested in acquiring Gordon, who was informed by the Browns on Saturday that they will be parting ways with him.
Gordon posted an Instagram story later Saturday in which he thanked the Browns and their fans.
"Huge s/o to the city of Cleveland," Gordon wrote. "This place will always feel like home to me.. I'm extremely honored and blessed to have been able to grow up and start a life amongst such a passionate and motivated group of individuals.. It's been a hell of a journey with you guys. I wish all of you nothing but the best.. Thanks to the @ClevelandBrowns organization for having me, I'll never forget my time here.
"Same book, next chapter... P.S. Anybody need a deep threat WR??"
Gordon is a vested veteran and is not subject to waivers.
If the 27-year-old Gordon is released by the Browns, he will become a free agent.
If another team trades for Gordon, he will play this season for his minimum salary of $790,000 and can be tendered after the season.
The Browns previously said he would not play in Sunday's game against the New Orleans Saints because of a hamstring injury.
Gordon was late arriving at the Browns' facility Saturday and "was not himself," NFL sources told cleveland.com. He showed up complaining of a pulled hamstring despite being fine in practice Friday, according to the sources.
He wasn't listed on the injury report Friday, and hadn't been on it all week.
The sources also said that when doctors examined his hamstring Saturday, it was evident that perhaps he was on the verge of relapsing or had relapsed.
"(On Saturday) afternoon we informed Josh Gordon and his representatives that we are going to release him on Monday," Cleveland general manager John Dorsey said in a statement. "For the past six years, the Browns have fully supported and invested in Josh, both personally and professionally and wanted the best for him, but unfortunately we've reached a point where we feel it's best to part ways and move forward. We wish Josh well."
Gordon sat out the 2015 and 2016 seasons plus all but the final five games last year because of suspensions related to violations of the NFL's substance abuse policy. He had 335 receiving yards and one touchdown in 2017.
The 6-foot-3, 225-pound Gordon missed much of the preseason while completing a health treatment program.
Gordon started last Sunday's 21-21 tie with Pittsburgh in Week 1 that snapped the Browns' 17-game losing streak. His only reception was a 17-yard touchdown pass from Tyrod Taylor late in regulation to force overtime.
Gordon has missed 56 of a possible 97 games. He played only 11 games since the start of 2015.