It has been suggested that the ambitious Bianconeri are keen on bringing a prolific Egyptian forward onto their books in Turin.
In an effort to tempt those at Anfield into a deal, Argentina international Dybala has been mooted as a potential makeweight.
His arrival at Anfield, along with a sizeable fee, would help Liverpool to counter the loss of a talismanic presence.
Rush, though, cannot see Jurgen Klopp agreeing to part with a man tied to fresh terms last summer and one who remains a vital figure in the Reds’ future plans.
He told Corriere di Torino: “I think Salah will stay at Liverpool.
“The fans love him and he is fine here. He signed a new contract, I do not think the exchange will be made.”
While Salah is unlikely to be heading to Italy any time soon, Arsenal midfielder Aaron Ramsey will be treading that path at the end of the season.
He has a lucrative pre-contract agreement in place with Juve as he prepares to drop into the free agent pool.
Rush believes a fellow Welshman is making the right career call as he is eager to get his hands on major silverware.
“He’s a fantastic player, a very reserved person, a man of the family. Juventus care a lot about how their players act off the pitch and he’s a genuine person, the right man for the Bianconeri,” said Rush.
“Why Juve? I spoke to him a couple weeks ago, he’s always been convinced of this choice because he wants to win trophies and Juve has always been the first choice for him. He believes that they have more chances to win than other teams.”
When Ramsey arrives at the Allianz Stadium, he will be linking up with five-time Ballon d’Or winner Cristiano Ronaldo.
Rush is excited to see the pair in action, with a Portuguese superstar proving that he made the right call in delaying a move to China in order to prolong a stunning career in Europe.
“He's a fantastic football player, maybe the best in the world,” said Rush.
“He could have chosen China but he came to Italy, it was a big step for him. When Ramsey is there, I cannot wait to come to Turin to see them play together.”