The 26-year-old is expected to sign a four-year contract with an option for a further year, with his medical provisionally scheduled for Monday.
Anthony enjoyed a productive campaign last season, scoring nine goals and providing four assists in 38 appearances across all competitions, although Burnley were unable to avoid relegation.
The London-born winger, who began his career in Arsenal’s academy before spells at Weymouth and Leeds United, is understood to be attracted by a return to the capital.
Brentford boss Keith Andrews views him as a strong tactical fit. Anthony would become the club’s second major signing of the summer after Jannik Schuster arrived from RB Salzburg.
