Hodgson faces a stiff task following a disappointing season last term and one of his first jobs will be to persuade the club's top stars to stay on Merseyside.
Murphy, who is being linked with a move back to Liverpool along with Hodgson, is a big admirer of the 62-year-old's management style and feels he is the right fit for the Reds.
"Liverpool need someone who has an understanding of the history and heritage that lies behind the club and what it means in the context of English football," Murphy told the Daily Mirror.
"People spoke about Mourinho, but I personally didn't see him as an ideal fit with Liverpool, because right now, they need someone who has an empathy for the club.
"I admire Roy Hodgson. He has a philosophy of playing good football which will fit well at Liverpool, and he gives players responsibility and a platform to work from
"Maybe it is time Liverpool had an English manager who knows about the club."