The Mirror says Hodgson will fly back from the World Cup today, hoping to swiftly finalise arrangements to become the next Liverpool manager.
The Fulham boss has been identified as the Anfield club's number one target to replace Rafa Benitez, and the Reds board rubber-stamped an official move for him last Friday.
Talks have been held up by Hodgson's role as a TV pundit working for the BBC in South Africa, and there are still some loose ends to tie up.
But with Hodgson due back in London this evening, club officials still expect to make an official announcement imminently and most probably within the next 48 hours.