Rush is good friends with Salah's agent Ramy Abbas.
“Each time the conversation usually switches to Mo and his future. I've constantly insisted that Mo can become a true Liverpool legend if he stays for another three years and maintains his incredible standards.
“You need to keep performing for 10 years at the highest level. Mo can now achieve that."
Rush has also had quiet but pertinent chats with Salah who is an admirer of the Welshman.
Liverpool's all-time record goalscorer Rush added: “I keep telling him if he stayed he could smash my records. I also said that the grass isn't always greener on the other side.
“I was so glad that I came back to Liverpool where I was loved.
"Everyone at Liverpool including the fans love him. This is like a new signing. I am absolutely delighted. Hopefully, in my role as Liverpool ambassador, I've helped in some way. I honestly would love it if he becomes a record-breaker at Liverpool."