New West Brom head coach Alan Irvine has made a new striker one of his top priorities this summer as he looks to bolster the attacking options at The Hawthorns, and Deeney is thought to figure prominently on his wanted list.
West Brom are desperate to bolster their strikeforce with Nicolas Anelka leaving the club last March and Matej Vydra and Thievy Bifouma both returning to their parent clubs after loan spells.
A number of clubs are keen on signing Deeney this summer, with the player regarded as one of the best front-men outside the Premier League.
Deeney has broken through the 20-goal barrier in each of the last two seasons and Watford are bracing themselves for offers..
Norwich City are thought to have had a £5million bid rejected for Deeney this summer, while the likes of Swansea City, Aston Villa and Burnley are all hoping to lure him away from Vicarage Road.
However, West Brom are hoping to steal a march on their rivals by making a move for the midlands-born hit-man as Irvine looks to bring in a proven goalscorer to solve the club's problems in the final third.