Henry, 23, emerged as one of the best full-backs outside of the top flight last season with a series of impressive displays before Brentford ultimately fell just short of promotion from the Championship.
A number of Premier League clubs have shown interest in the left-back over the summer but found the Bees reluctant to do a deal for the player.
West Ham had also been tracking the player as they search for a new left-back but have been forced to put their interest on hold while they try to prioritise bringing a new centre-back in with finances tight.
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