Albion are keen to boost their options at left back and Henry's impressive displays for the Bees last season in the Championship has impressed Albion head coach Graham Potter.
Dan Burn was the main man at left back for Albion last season as the 6ft 7in centre back made an unlikely but largely successful transition to the world's tallest left back.
Brazilian Bernardo also filled in when required while Solly March and even Steven Alzate were used at left wing back when Potter went with three at the back.
The fact Henry, 23, is equally comfortable as a left wing back as he is at left back is a crucial factor in Brighton's pursuit of the former Walsall man.
Albion are not alone in the race to sign Henry with Aston Villa and Leeds also said to be keeping a very close eye on developments. Villa boss Dean Smith managed Henry during his spell in charge at Brentford.
Henry was excellent last campaign as his displays helped the Bees to the play-off final where they lost out to Fulham.
He signed for Brentford from Walsall in 2016 for £1.6m and Bees boss Thomas Frank is keen to keep hold of his key man.
"Rico is one of our most talented players.
"We all know how difficult it is to find good left-footed full-backs and wing-backs and he’s one of the most talented in the division. So we definitely want to keep him longer term.”
Brighton also remain in the market for a striker and have registered their interest in a loan move for Liverpool's Rhian brewster and a permanent deal for Ameria's £18m rated Uruguay international Darwin Nunez.