Kelleher has played in 25 Premier League games for Liverpool since making his debut five years ago.
He has also played in more than 40 cup games for the club, which means he has won two Premier League titles, the Champions League, FA Cup, two League Cups and a Uefa Super Cup in his time at Anfield.
Netherlands international Flekken joined Brentford from German side Freiburg for a reported £11m in May 2023.
He had kept more clean sheets than any goalkeeper in the Bundesliga over the previous two seasons and has only strengthened his reputation while at Brentford.
Flekken has played in all but two Premier League games over the past two seasons, registering 14 clean sheets and three assists.
