Salah, 26, left Serie A rivals Roma in 2017 to join the Anfield club and has been one of the best players in the world over the last 18 months.
And they believe the second-biggest transfer fee of all time could persuade Liverpool to sell their star man.
Since arriving for a bargain £34.3m, Salah has scored 64 goals for the Reds, including 45 last season as Liverpool reached the Champions League final.
His side are second in the league, level on points with Manchester City, but have a game in hand on the reigning champions.
After two years at Chelsea, in which he was loaned out twice, he joined Roma in 2016 and enjoyed a stellar season before being picked up by Jurgen Klopp.
Ronaldo, 34, joined Juventus from Real Madrid last summer and the thought combination of him and Salah will have defences across Europe on red alert.
The futures of both Paulo Dybala and Douglas Costa are in doubt, which would pave the way for Salah to walk into the Juventus starting XI.
Dybala had a bust-up with manager Massimiliano Allegri last week and is today said to be edging closer to a move to Real Madrid.
Meanwhile, Costa put Manchester United on alert after liking a Twitter post linking him with a move to Old Trafford.