The Egyptian is off contract this summer and free to ink terms on a pre-contract deal with any foreign club from January 1, ahead of leaving in a Bosman transfer in June.
L'Equipe says PSG are in contact with Salah and his representatives about a move to Paris next year.
And there is a growing confidence that the 32 year-old is keen on the prospect.
After his man-of-the-match performance in victory over Manchester City last night, Salah said: "Until now this is the last City game I will play for Liverpool so I was just going to enjoy it.
"The atmosphere was incredible so I will enjoy every second here. Hopefully we just win the league and will see what will happen."
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