The 26-year-old has become a permanent fixture in the Potters’ back line since joining for £6 million from Middlesbrough at the start of last season.
Hodgson is now believed to be willing to test Stoke’s resolve with a £5m bid in January for the defender, but may have to pay more if he is to eventually land his man.
Liverpool have struggled for numbers defensively this season and Jamie Carragher is not expected back from his shoulder injury until February at the earliest.
Daniel Agger has missed much of the campaign with a calf problem, while Glen Johnson and Fabio Aurelio have also suffered with injuries this season.
Huth's team-mate and central defensive partner Ryan Shawcross has also been linked with a move to Anfield in recent times.