Following on from news that new summer signing John White will skipper the Shrimpers in the new season, the 33-year-old defender has been told he is surplus to requirements at Roots Hall.
Brown left no room for sentiment with Barker but has not ruled out the defender still having a future with the Sky Bet League Two side should his trial period with the Bulls bear no fruit.
"I've had a conversation with Chris and explained how we're moving in a different direction now and that it may be best for him to move on," the former Hull manager told the Southend Echo.
"He's a great lad but we'll see how he gets on with Hereford and take things from there.
"If he's still with us by the time we get back from Madrid then he could still have a future with us."