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Take a look at Caoimhin Kelleher's best saves in the Premier League?
Brentford had been facing competition from other clubs for Kelleher, including Leeds and West Ham, but Thomas Frank's side have a strong relationship with Liverpool, having secured Sepp van den Berg and Fabio Carvalho from Anfield last summer.
Kelleher, capped 22 times by his country, secured a second Premier League title with the Reds this season but only started 10 games as Alisson continued ahead of him in the pecking order.
Flekken completes Leverkusen move
Elsewhere, existing Bees No 1 Flekken has completed a move to Bayer Leverkusen.
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Leverkusen and Brentford agreed a fee in the region of £11m (€13m) inclusive of add-ons on Tuesday, meaning he will link up with former Manchester United boss Erik ten Hag in Germany.
Follow the transfer window on Sky Sports
The first of two summer transfer windows is upon us - and there is no better place than Sky Sports to get all the latest transfer news and rumours.
Use the Sky Sports app and website for all your updates in our dedicated Transfer Centre and Premier League club blogs, plus live Q&As with our reporters throughout the summer.
The Transfer Show returns to Sky Sports News from Sunday June 1 for the start of the pre-Club World Cup window and will then be on every weeknight at 5pm and 7pm until the deadline on Tuesday June 10.
The summer transfer window will open again on Monday June 16 until Monday September 1 - with the deadline brought forward to 7pm this year.
For more news relating to Manchester United, visit our sister site MUFC Live.