Senior figures at the club believe it is worth making one more try to sign Salah but others are advising they should give up until next summer.
Any new offer would need to be approved first by the SPL through interim chief executive Saad Al Lazeez and director of football Michael Emenalo.
Liverpool rejected a verbal offer for Salah worth up to £150m from Al Ittihad on Thursday.
Liverpool’s position has not changed – Salah is not for sale.
Speaking after Sunday’s 3-0 won over Aston Villa, Jurgen Klopp said: “I never had any doubts about his commitment to this club. You can’t imagine how much fuss the world has made but how calm we are with it. He is our player and he wants to play here.”
The SPL window closes midnight on Thursday.
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