Earlier this week, an arbitrator upheld the NFL's one-year suspension of Gordon for failing a marijuana test. Gordon is not allowed to practice with the team or take part in team activities.
"From what I heard we can't communicate with him but I'm going to try to find a way," Burleson said after the Browns' preseason finale Thursday night. "I want to let him know we've still got his back and he's family."
Starting quarterback Brian Hoyer offered similar words of support for Gordon.
"Obviously we all feel for Josh," quarterback Brian Hoyer said. "He's a teammate that we're going to be there to support throughout this entire difficult situation for him."
Cleveland is expected to start free agent acquisitions Andrew Hawkins and Miles Austin at receiver this season.
First-year head coach Mike Pettine said the team has done a good job dealing with Gordon's suspension.
"We addressed it, but it wasn't necessarily a challenge," Pettine said. "I just think everybody kind of knew the day was coming. I think the players did a good job kind of compartmentalizing things and not letting it become a distraction."
The Browns open the regular season Sept. 7 against the Pittsburgh Steelers.
- Paul Palladino