Bilic made no secret of his admiration of the player, having recently praised Hogan and fellow transfer target Jermain Defoe and it is understood that the Hammers have had a £10m bid rejected by the Championship club.
Hogan has been in fine form this season, having scored 14 goals in 26 games and is attracting from the Premier League and abroad.
Besides West Ham, Watford are also reported to be interested and Bundesliga high-flyers RB Leipzig are also said to be tracking Hogan.
Brentford are thought to be asking for £15m for the striker and it remains to be seen whether teams will be prepared to pay the Bees' asking price.