Salah, 31, has just one year left on his contract with Liverpool after the current season.
The Reds rejected offers of over 200m from Al-Ittihad and Al-Hilal last summer.
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TalkSPORT says Al-Hilal are planning to make a bid in excess of 70m.
Al-Hilal is also said to have presented a lucrative three-year contract to the player.
It is not clear how much Salah is being offered, but he would be one of the league's highest paid players.