The 23-year-old helped the Bees to the final of the Championship play-offs last season and is attracting interests from top-flight clubs.
West Ham United have also been linked with Henry as boss David Moyes wants an upgrade on Aaron Cresswell and Arthur Masuaku, but they have had to put their interest on hold as they now prioritise signing a new centre-back.
The Hammers are skint and Villa could use that as an advantage to land the Brentford star ahead of them.
Henry assisted thrice in 49 Championship games last term, and his attacking and defensive qualities have attracted the Villans and West Ham.
Smith knows the left-back well from their days together at Walsall and Brentford, and a second reunion could be on the cards.
Villa currently have Matt Targett and Neil Taylor as their options at left-back, but the manager reckons he could do with another top addition in Henry.
He has already signed right-back Matty Cash from Nottingham Forest, and another full-back could soon be arriving from the Championship as Villa look to impress this season and prevent another relegation battle.