Clarets ready to break club transfer record for striker Gray
The 24-year-old was believed to be on his way to Bristol City, but has been unable to agree personal terms with the Robins.
In the meantime, the Clarets are believed to have stepped in and had an offer accepted by the Bees.
The fee will dwarf the previous club record of £3million Burnley paid out for Steven Fletcher from Scottish side Hibernian in 2009.
That figure was equalled at the start of last season when they bought winger George Boyd from Hull.
Clarets boss Sean Dyche has been active in the market over the summer, bring in a number of new players including Matt Lowton and Jelle Vossen.
He has also been hoping to add Nottingham Forest skipper Henri Lansbury to his squad, but the midfielder looks set to stay at the City Ground despite a £4m. bid.
Gray joined the Bees last summer for £500,000 from Luton Town, after hitting 52 league goals in 97 appearances for the Hatters.
He has already notched two goals in two appearances this season as Brentford have opened the campaign with a win and a draw.
The centre forward is well known to Burnley’s new director of football Frank McParland, who was pivotal in bringing the player to Griffin Park.
It is believed Gray is undergoing a medical at Turf Moor ahead of the proposed record deal.