The 20-year old Czech Republic defender played a bounce match for the Shrimpers last week before trialling with the League Two outfit for two days.
Brown admits that Sokolik has impressed at Roots Hall and suggests the Reds centre-back may be offered a deal.
"I need to talk to a couple of coaches but hopefully those discussions will be positive," Brown told the Echo.
"Jakub has done well and I've certainly been impressed by him."
Southend currently sit seventh on the tier four table but have not win in their past nine league outings.
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