The Reds kept hold of Salah, 31, in the summer despite Saudi side Al-Ittihad testing the club's resolve with a £150million offer.
But there is an expectation the Middle East outfit may return for the Egyptian in January or at the end of the season.
It is understood they are keen for Salah to be the face of the Saudi Pro League.
If he does depart Anfield, Jurgen Klopp will want to replace the void left by Salah - who has contributed 192 goals and 83 assists in 315 games.
According to The Mirror, former Manchester City man Sane, 27, is their top priority.
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