Al-Ittihad are in talks with the Reds over a £40m deal for the Brazilian, who has not made the trip to Germany for a pre-season training camp while negotiations rumble on.
Fabinho is understood to have agreed personal terms with Nuno Espirito Santo's side, who are now discussing the key details of the deal with their Merseyside counterparts.
While there is still work to be done before Fabinho can be released from his Liverpool contract, the Reds will not stand in his way of a departure if the price is right.
Southampton's Romeo Lavia and Brighton & Hove Albion's Moises Caicedo have both been linked with switches to Anfield as a replacement for Fabinho, but the duo could both prove too expensive.
Lavia could command in excess of £50m to depart St Mary's, while Brighton are supposedly prepared to hold out for a nine-figure sum to sell Caicedo, who is also on the radar of Chelsea.
Having already added Dominik Szoboszlai and Alexis Mac Allister to their ranks for a combined £95m, the Reds may instead seek out a cut-price alternative to Lavia and Caicedo, especially with talk of a new centre-back also arriving at Anfield.
Liverpool manager Klopp is believed to have chaired a meeting to discuss bringing Fiorentina's Amrabat to Anfield after the World Cup, where the midfielder shone during Morocco's historic run to the last four.
According to The Athletic, Liverpool are still interested in signing Amrabat this summer, as the 26-year-old could potentially be allowed to make his exit from La Viola in the current window.
As things stand, Amrabat could leave the Europa Conference League finalists as a free agent
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