By Wayne Veysey | Chief correspondent
The former Charlton and West Ham manager, who has been out of work since his acrimonious departure at Upton Park in September 2008, is one of four bosses on Fulham’s radar if Hodgson takes over at Anfield.
The Craven Cottage shortlist also includes Sven-Goran Eriksson, Mark Hughes and Tony Mowbray.
Eriksson is believed to be the frontrunner because of his vast experience but there is also strong support for a training ground-style manager in the Hodgson mould who can maximise the resources at his disposal and improve the players in the squad.
Curbishley has not managed since leaving West Ham but that is partly because of a drawn-out compensation battle with the club. The 52-year-old won a case for constructive dismissal last November but the final £2.2 million bill was not settled until new owners David Sullivan and David Gold bought the club.
Nevertheless, he still has a good reputation in the game and is understood to be keen to get back into top-level management.
However, it is by no means certain that Hodgson will replace Rafael Benitez at Liverpool. It is understood that the Fulham manager, who returns from South Africa today after being a pundit at the World Cup for the BBC, is still considering whether the attraction of taking over a Champions League calibre club is outweighed by the instability in the boardroom.
Owners Tom Hicks and George Gillett have put the club up for sale and Hodgson has told friends that there are “a lot of issues not just around the team, but also the ownership”.
The Liverpool board are also aware that there are misgivings among supporters about Hodgson’s credentials for managing one of the world’s biggest clubs.
Although the 62-year-old has achieved great success at mid-ranking clubs, particularly in Scandinavia, and on the international scene during his 34-year managerial career, the only elite club he has managed is Inter Milan, where he had mixed results.
Hodgson was unwilling to commit himself to Liverpool before England’s game against Slovenia on Wednesday but their progress to the knockout stages has diminished the possibility that Fabio Capello will quit as manager, whatever happens in Sunday’s clash against Germany.