Speaking to Liverpool Echo, Rush said: "Without doubt [Salah remains integral], I was really made up when he signed the new contract. The first half of last season, you know, he was incredible, and in the second half it was probably more about his assists. He is changing his game now to do that.
"What I like about him now, ever since he was injured when he did the shoulder (in 2018), you look at his physique and he is not going to get injured again.
"His determination to be successful is there and when you speak to him, he is looking to learn and most probably the best part about him now is he is helping the younger ones as well.
"[He tells them] 'If you want to be doing that, you need to be doing this'. So he is an inspiration to the younger players to tell them if you want to achieve what Mo Salah has achieved, this is what you have to be doing.
"You have to work hard in training, you have to do that and maybe sometimes that goes unnoticed about such a great job that he has done.
"That is why I am happy he has signed for two years and looking at his performances, I look at the [ages] of 28 and 29 and you work on your weaknesses and over the age of 30 you are taught to work on your strengths. And I think that is what Mo is doing and, as I say, it goes unnoticed about the work he helps the younger ones off the pitch.
"One hundred percent [he should be vice captain] and he captained them against Preston didn't he? I think Van Dijk is doing what Van Dijk does, he is incredible and he leads them there."