But Reds boss Jurgen Klopp remains keen on adding the Egypt winger to his attacking option.
Roma want around £40m for Salah, who scored 15 goals in 31 league appearances for the Serie A side this season.
He came close to joining the Reds back in 2014 before opting to sign for Chelsea.
However he failed to impress at Stamford Bridge and was sent to Italy, where he has rejuvenated his career.
Liverpool fans worried about Mohamed Salah after snub Fri, June 2, 2017
Liverpool fans aren't overly-excited to sign Mohamed Salah…
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Is Mohamed Salah on his way to Liverpool?
Salah had spells at Fiorentina and Roma on loan, before signing a permanent deal to play at the Stadio Olimpico.
It had been rumoured Salah may be in Liverpool to tie up a deal.
But his agent Ramy Abbas Issa insists the 24-year-old is currently in Egypt and hasn't left the country following his arrival at the end of the season.
Issa tweeted: "M. Salah has not left Egypt since he last arrived there from Rome following end of the season."
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