Hodgson will be aware that popular support for Kenny Dalglish, his long-time friend, to become Benítez's successor is growing on Merseyside, with the Liverpool legend having made it clear that he would like to be considered for the position.
While Hodgson has not made a decision to leave Fulham, it is understood that he would like to hear what Liverpool have to say.
Liverpool, though, are comfortable with the way that their recruitment process is going, the desire to ensure that they attract the best possible manager available overriding any yearning to make a hasty appointment that they could come to regret.