Andrews has been part of Frank’s coaching staff since last year and is well-regarded within the club.
Frank left Brentford after seven years in charge on June 12 to become Tottenham’s new head coach.
Brentford promoted from within last time, with Frank having been Dean Smith’s assistant.
Andrews is one of a handful of names Brentford are seriously considering – but a final decision has not yet been made.
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Andrews is known for being Brentford’s set-piece specialist, but his coaching ability extends far beyond just that. He has been a coach at MK Dons and Sheffield United and also worked as an assistant for the Republic of Ireland U21 and senior sides.
During Andrews’ 16-year playing career, the former midfielder represented the likes of Wolverhampton Wanderers, MK Dons, Blackburn Rovers and Bolton Wanderers, as well as being capped 35 times by the Republic of Ireland.
Ipswich boss Kieran McKenna is among a number of other coaches admired at Brentford.
Scott Parker is not under consideration, contrary to reports elsewhere.
Sky Sports to show 215 live PL games from next season
From next season, Sky Sports’ Premier League coverage will increase from 128 matches to at least 215 games exclusively live.
And 80 per cent of all televised Premier League games next season are on Sky Sports.