The deal is a straight loan for the 27-year-old, who signed a new contract until 2031 last year.
The Uruguay international joined Barcelona B in 2018 before being promoted to the first team in 2019.
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The centre-back will add to Andoni Iraola's options at the heart of his defence following the departure of Ibrahama Konate to Real Madrid and fitness concerns over relatively inexperienced 21-year-old Jeremy Jacquet.
The summer signing from Rennes has made fewer than 100 senior career appearances and has not featured in pre-season yet after missing the second half of last season following shoulder surgery.
Joe Gomez suffered a muscle injury in Liverpool's opening pre-season game, while teenage centre-back Giovanni Leoni is still recovering from an ACL injury, leaving captain Virgil van Dijk as Liverpool's only fully fit senior centre-back.
Araujo joined Barcelona from his native Uruguay in 2018 and made his debut the following October, going on to play more than 200 games at the Nou Camp to date.
Liverpool's Barcola deal difficult to complete after talks with PSG
Liverpool have held preliminary talks with Paris Saint-Germain over the possibility of signing Bradley Barcola.
However, Sky Sports News understands that there is a significant gap in valuation between the two clubs.
The Champions League holders value the 23-year-old at £145m.
PSG's stance on the fee makes it a difficult deal to complete at this stage.
