Brown is being released by the Gunners at the end of the season.
He is now testing with West Ham's U18 team, reports Jeorge Bird's Arsenal Youth website.
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Brown is the son of former West Ham fullback and coach Kenny Brown. Brown Snr is now West Ham's academy manager.
The youngster featured for the Hammers' U18 side in their 4-2 win against Aston Villa last weekend.