The 24-year-old is on the verge of reuniting with former Bees boss Uwe Rosler at Elland Road after completing a medical at the club’s training ground on Monday.
Sky sources understand Dallas will be announced as a Leeds player on Tuesday and moves for an undisclosed fee after starring under Mark Warburton at Griffin Park last term.
Dallas joined Brentford in 2012, signed by Warburton while he was sporting director, and played under Rosler before the German moved to manage Wigan in 2013.
Warburton, Rosler’s successor, played Dallas 43 times last season and he rewarded him with eight goals, including two stunners in an away victory at Fulham, while he also bagged his first international goal for Northern Ireland.
Warburton first spotted Dallas playing for Irish side Crusaders, where he scored 24 goals in 67 league games.