However, a Browns team source told Schefter that the team is not looking to trade Gordon.
Gordon said Tuesday that he doesn't want to be traded.
"I haven't heard too much about it," Gordon said. "Cleveland is my team. That's where I want to be, everything like that. That's not even in the ballpark for me. I'm not sure how that works."
Cleveland has tried to establish an environment in which Gordon could thrive, and many around the league believe first-year head coach Hue Jackson is the right coach for him.
"This is where I want to be and I'm happy to be with Cleveland."Josh Gordon
"I think it works out perfectly then for me," he said. "Mr. [Jimmy] Haslam, the organization, Coach 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."
Gordon took part in three series with the Browns' starters in Sunday's practice.
Gordon, 25, is suspended for the first four games to start the regular season, but the NFL is allowing him to participate in team activities during the ban.
Gordon led the NFL with 1,646 receiving yards in the 2013 season but was suspended for 27 of the next 32 games for violating the NFL's substance abuse policy. He has 161 receptions for 2,754 yards and 14 touchdowns in 35 career games, all with the Browns.
ESPN Browns reporter Pat McManamon contributed to this report.