Byrd was believed to be unhappy at the Bills following a contract dispute during the off-season, leading The Buffalo News to report that he has requested a trade, citing an executive of a different NFL club as their source.
However, Brandon insists that there is no truth in the rumours and that the Bills' main focus is to get the currently-injured Byrd back playing again.
"There was no trade requested. That isn't even a topic of conversation in this building. I know these reports come from all over the place. I don't know where they come from at times," Brandon told The Howard Simon Show.
"We always listen to anything from our fellow clubs, [but] our focus is seeing [Byrd] get back on the field. He's nothing but a true professional, and he's a great teammate."
The Bills designated Byrd as their franchise player in February of this year.