The club has already made contact with Liverpool to express their interest in Kelleher this week. This move comes as Brentford considers the future of their current goalkeeper, Mark Flekken, who has attracted new interest from a Bundesliga club.
Brentford is exploring options to find a suitable replacement for Flekken, and Kelleher has emerged as a potential candidate. He is also being considered by West Ham and promoted Leeds United.
Bayer Leverkusen, under their new coach Erik ten Hag, is in talks to sign Flekken, which has prompted Brentford to consider alternative options.