Murphy said: "I admire Roy Hodgson. He has a philosophy of playing good football which will fit well at Liverpool. He gives players responsibility and a platform to work from. Maybe it is time Liverpool had an English manager who knows about the club."
Murphy flourished as Cottagers captain under former Inter Milan and Blackburn manager Hodgson.
Murphy added: "Roy is a talented manager who succeeds because he works incredibly hard. He instils confidence in his players and has a style the players can enjoy. His success has been a mix of a lot of things but primarily hard work."