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The Swans sacked Bob Bradley earlier this week after a 4-1 home defeat to West Ham left them 19th in the Premier League, four points adrift of safety.
Ryan Giggs and Chris Coleman are the frontrunners to succeed Bradley, but Murphy reckons Hodgson is the ideal fit for the struggling Welsh club right now.
The 69-year-old's reputation took a hammering after he quit as England boss following a disastrous showing at Euro 2016.