Andrews, who joined Brentford in 2024 as a set-piece coach, is now the frontrunner for the managerial position.
The 44-year-old is highly regarded within the club and is reportedly assembling a coaching staff for the upcoming Premier League season.
This potential appointment aligns with Brentford's history of promoting from within, similar to Frank's succession of Dean Smith.
Several other candidates, including Justin Cochrane and Kieran McKenna, were considered, but Andrews is now the likely successor, marking his first managerial role.