The 25-year-old, a summer signing for Gary Bowyer's side from Notts County, has made just 12 appearances for Rovers and has found himself down the pecking order with the likes of Tom Cairney showing such impressive form.
But Brentford boss Mark Warburton believes the midfielder can boost the Bees' promotion hopes.
"Alan was an outstanding performer at Notts County last year, and thoroughly deserved his move to Blackburn Rovers, where he has continued to show excellent form," Warburton told the club's official website.
"He is a good Championship player and is a positive addition to our squad.
"Alan offers us options, both wide and centrally, and I am sure he will add real value to the first-team squad in the weeks ahead."