Brown failed to catch his lone target in Sunday's 21-14 loss to the Jets.
Brown remains Houston's top tight end in terms of playing time because of his run-blocking skills, but he's taken a back seat to rookie Brevin Jordan as a receiver. Jordan caught three passes including a touchdown Sunday while playing an equal number of snaps (34) as Brown. The rookie is part of Houston's future, while the 27-year-old Brown is on a one-year deal.