The team's head of football operations, talking to a group of Cleveland-area reporters in Tampa, Florida, did not deny there were conversations with multiple clubs about Gordon but the idea the team was willing to listen to offers was "probably a mischaracterization."
A Browns team source had told Schefter that the team was not looking to trade Gordon, but Brown's comments Thursday were the first public comments from the organization on trade speculation around Gordon.
"I understand what the interest is in Josh. There are literally hundreds of conversations going around the league about players all the time," Brown said.
Gordon will serve a four-game suspension to start the regular season and is one violation away from another indefinite suspension, per the league substance abuse program. Brown said Thursday that Gordon?is doing well.
"He's working hard. He's in with his teammates. I think he understands the position he's in and what the opportunity is here with the Browns. He's serious about wanting to get back in the league and obviously for him getting back with his teammates here has been a great thing. We talk to him regularly and he's doing well.
"We see Josh as a great weapon for our offense. He's still working himself back into shape. He's done a good job getting on top of the playbook. He's kind of come back in and I think even to his surprise feels much like a veteran in the room to some of the younger receivers.
"It's a young room, still, a lot of young guys trying to find their way and prove themselves. So he's actually found himself quite a leadership role coming back and we see him as a guy who can be a dynamic piece in our offense."
Gordon said Tuesday he didn't want to be traded after returning from his one-year suspension and finding a head coach, an offense, and an infrastructure in place to see through his career comeback.
"I think it works out perfectly then for me," he said. "Mr. [Jimmy] Haslam, the organization, Coach [Hue] Jackson, I think the world of those guys, this city, this organization. They're family. 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."
ESPN Cleveland's Tony Grossi contributed to this report.