Can a player be traded with an injury designation?

Just say the players you think will be traded!
Payton Turner was suggested as a tradable asset elsewhere on the web. He’s the player I had in mind considering no one saw him get injured, he has trade value, and unlikely to get a new contract unless he has a big season without health issues. I don’t think he’ll be traded, but it seems possible that if they wanted to trade him, they might shut him down this week.