But they face competition from Leeds and Aston Villa.
Henry, 23, was outstanding last term as he helped the Bees all the way to the play-off final.
But the West Londoners suffered defeat at Wembley to arch-rivals Fulham and now could be set to lose in-demand Henry.
Brighton are after a new left-back who can also play at left wing-back and Henry would fit the bill.
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