The Mail on Sunday says Liverpool plan talks with 62-year-old Hodgson in the next 48 hours.
But many fans want to see Kenny Dalglish in charge and past players have been queuing up to support his claims, to the irritation of some powerbrokers at the club.
Some at Anfield prefer Hodgson to Dalglish, seeing him as the safe pair of hands needed to bring stability after a turbulent year.
But others are concerned that Hodgson's only experience at such a big club came more than a decade ago with Inter Milan.