Liverpool captain Jordan Henderson has been included in the Reds' squad for their pre-season camp in Germany, but there is no space for Fabinho.
Jurgen Klopp's men will spend 10 days Baden-Wurttemberg as they ramp up preparations for the 2023-24 campaign, during which time they will take part in two friendly matches.
Liverpool open their pre-season against Karlsruher SC at Wildparkstadion next Wednesday, before heading to Sportpark Ronhof to meet Greuther Furth on July 24.
Klopp has called up a 32-strong travelling party for their summer sojourn to his homeland, including skipper Henderson, who has been heavily linked with a switch to Saudi Arabia.
Al-Ettifaq - who are now managed by Reds legend Steven Gerrard - are believed to have reached a verbal agreement on a mammoth contract with the 33-year-old, who could supposedly be in line for a £700,000-a-week wage in the Middle East.
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Henderson, who is believed to pocket a £200,000 weekly salary at Anfield, is reported to have been given the green light by Klopp to leave the club after 12 years of service, but the two clubs are yet to agree on a fee.
Liverpool still have their skipper under contract for another two years, and the Reds are not prepared to let him leave on a free transfer, which is what Al-Ettifaq were supposedly hoping for.
Reports claiming that a £10m bid could be enough are also thought to be wide of the mark, and Liverpool are instead thought to be holding out for £20m to let the England international depart.
Liverpool have purportedly used Kalidou Koulibaly's move to Al-Hilal from Chelsea for £20m as a reference point, and Al-Ettifaq are yet to approach the Merseyside giants with their opening bid.
As a result, Henderson could very well remain at Anfield beyond the end of the summer transfer window and will board the plane to Germany, but there is no space in the squad for Fabinho.
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Similarly to Henderson, the Brazil international - who experienced a sharp decline in form last season - is also said to be attracting interest from the Saudi Pro League, more specifically champions Al-Ittihad.
The Tigers - who have already welcomed Karim Benzema, N'Golo Kante and Jota to the club this term - are now understood to have submitted a £40m offer for Fabinho, who is still contracted to Liverpool for another three years.
The 29-year-old supposedly did not refuse to travel with the team, but all parties considered it best for the midfielder to stay at home, although his exit is likely to hinge on whether Liverpool can bring in a replacement.
Southampton's Romeo Lavia and Brighton & Hove Albion's Moises Caicedo have been touted as successors to Fabinho in the number six role, but Chelsea are still thought to be leading the race for the latter.
Liverpool have already reinforced their midfield with the signings of Alexis Mac Allister and Dominik Szoboszlai, both of whom have been named in the Reds' tour squad, while Nat Phillips and Caoimhin Kelleher have also been included despite speculation surrounding their futures.
LIVERPOOL PRE-SEASON TOUR SQUAD IN FULL
Alisson, Gomez, Van Dijk, Konate, Thiago, Diaz, Szoboszlai, Nunez, Mac Allister, Salah, Adrian, Henderson, Gakpo, Jota, Tsimikas, Robertson, Matip, Bajcetic, Phillips, Kelleher, Alexander-Arnold, Pitaluga, Bradley, Clark, Doak, Frauendorf, Jaros, Koumas, McConnell, Mrozek, Quansah, Scanlon