Newcastle are still winless after eight rounds of Premier League action this season, lying in 19th position with just three points to show for their efforts.
Manager Steve Bruce is under huge pressure and is expected to be fired sooner rather than later.
The Magpies were recently taken over by Saudi Arabian consortium Public Investment Fund and are expected to hire a new manager and spend big in the January transfer window.
Hodgson left his role as Crystal Palace manager at the end of last season, with the 74-year-old signaling his intentions of not returning to top flight football.
The former England manager has saved the likes of Fulham, West Bromwich Albion and Crystal Palace from relegation in the past and Murphy, who played under the former Liverpool boss at Craven Cottage, would like Newcastle to hire him to prevent a drop down to the second tier.
Speaking on talkSPORT on Monday, Murphy said: “I know for sure the players would like him and be on board with him. You can’t not.
“He’s been there, done it, he took Palace from an impossible position, they were in a much worse position than Newcastle are by the way, and kept them up comfortably.
“He knows what he’s doing, he’s been in many relegation fights, time at Fulham, time at West Brom.
“Of course, with his age and what Newcastle want to do it is a short term thing but the other option is to try and go out and get the men you want to move the club forward and give them the project long term.
“But, which top manager is going to want to take that risk right now.
“People talk about Conte, who is a very capable manager but apparently he’s saying he’s not interested.
“The reason he’s not interested is because he doesn’t want to waste a year in the Championship.”
