The 26-year-old is keen to remain in the Premier League after Burnley’s relegation to the Championship last season, with several top-flight sides also monitoring his situation. According to the BBC, the Clarets are expected to demand around £20m for the Englishman, who impressed last campaign with nine goals and four assists in 38 appearances across all competitions.
Anthony began his career in Arsenal’s academy before breaking through at Bournemouth, is viewed as a strong tactical fit for Brentford head coach Keith Andrews.
He also spent time on loan at Weymouth and Leeds before joining Burnley permanently following their promotion.
Brentford, who finished ninth last season, have already strengthened with the signing of Jannik Schuster from RB Salzburg and continue to reshape their squad ahead of the new campaign.