The Mirror says the Egyptian king has put club top brass on red alert by declaring that he will review his situation next summer.
But after helping Liverpool win the Champions League and being feted as an Anfield hero, he feels the timing is wrong to leave Merseyside.
Manager Klopp was aware of the interest and has been involved in discussions with the club's hierarchy over the threat of the 26-year-old's possible departure.
There have also been enquiries from leading continental clubs for Salah's strike partner Sadio Mane.
Salah has indicated that he will review his situation next summer as he looks for one big final pay day.