"Listening (to trade offers) is probably a mischaracterization. We've said all we needed to say about it. We're not looking to trade Josh," Brown said Thursday, via the Akron Beacon Journal.
According to NFL Media's Mike Garafolo, the Browns spoke to teams about Gordon and their price for the wide receiver was "a second-round pick and then some," according to sources with knowledge of the situation.
Gordon hasn't played a game since December 2014 and will serve a four-game suspension to open the season.
The 6-foot-3 target is set to make his preseason debut Friday night versus the Tampa Bay Buccaneers.
Gordon said Tuesday he doesn't want to be traded.
"Cleveland is my team. That's where I want to be," Gordon told ESPN.com. "(Browns owner Jimmy) Haslam, the organization, coach (Hue) Jackson, I think the world of those guys, this city, this organization. They're showing me the love and respect back to me by allowing me to stay here up to this point.
"I expect to move forward with that. I'm excited about it. This is where I want to be and I'm happy to be with Cleveland."