The Reds turned down a mammoth £150m bid from Al-Ittihad on Friday a few hours before the English transfer window closed, but clubs in Saudi Arabia can still sign players until next Thursday.
Liverpool have supposedly said that Salah will not be sold under any circumstances this summer, but the Reds' stance has not deterred Al-Ittihad, who are thought to be planning an astonishing £200m offer.
Should Liverpool cave and accept such a bid, Salah would overtake Neymar as the world's most expensive player, and Al-Ittihad are apparently prepared to make him the highest paid footballer on the planet too.
While Liverpool swiftly turned down Al-Ittihad's £150m proposal, it is unclear if the Merseyside giants will be able to resist an unprecedented fee for a player who now has fewer than 24 months left to run on his contract.
A report from The Mirror claims that such a deal might be given the green light by Fenway Sports Group, who are aware that a £200m fee for a 31-year-old would represent a stellar piece of business from a financial viewpoint.
In contrast, Klopp is hoping that the owners stand firm and turn down Al-Ittihad's world-record approach, as the Liverpool boss will not be able to bring in a replacement until the window reopens in January.
Salah himself is not believed to be pushing for a move away, and his agent has often downplayed talk of an exit from Anfield, but the report adds that he has told friends that a lucrative Saudi Pro League transfer would interest him.
Nuno Espirito Santo's side are believed to be willing to pay Salah £1.5m a week, and he is also attracted to the idea of being the face of the Saudi Pro League.
Nevertheless, Klopp is still holding out hope that the former Chelsea and Roma man will continue in Liverpool colours this season, but an exit for the Middle East in 2024 might be "inevitable".
The Reds have already allowed Fabinho to join Al-Ittihad in a £40m deal, while Jordan Henderson and Roberto Firmino now represent Al-Ettifaq and Al-Ahli respectively.
Despite Firmino's departure, midfield additions took priority for Liverpool in the summer window, as Leighton Clarkson, Naby Keita and Alex Oxlade-Chamberlain also packed their bags and bid farewell.
After capturing Alexis Mac Allister, Wataru Endo and Dominik Szoboszlai - the latter of whom can also play in a more advanced role - Liverpool finalised their summer business with the £34.2m signing of Ryan Gravenberch from Bayern Munich.
As a result, Klopp is working with an identical set of senior attackers in Salah, Luis Diaz, Darwin Nunez, Cody Gakpo and Diogo Jota, although 17-year-old Ben Doak has now been integrated into the first team.
Liverpool will endeavour to maintain their unbeaten start to the new season at home to Aston Villa on Sunday, although Gravenberch is not expected to make his debut this afternoon.