Although Liverpool have lined up Hodgson to succeed Rafael Benitez at Anfield, sources close to the 62-year-old say he would prefer the challenge of being the England boss.
Hodgson is believed to view the England position as a more stable role and one which he believes he is ideally qualified for, given his 34 years in management and experience of managing Switzerland and Finland at international level.
The FA see Hodgson as an attractive candidate because, unlike novice international bosses, he would be able to hit the ground running.
Yet with Liverpool ready to appoint Hodgson when he returns from his BBC pundit’s position in South Africa later this week, there is only a small window for Soho Square to act.
Less than three weeks after removing an escape clause from a contract which expires in 2012, Capello is expected to resign should England fail to secure a place in the last 16.
Cottage swap | Hodgson is likely to leave Fulham, with Eriksson No.1 to replace him
Hodgson’s misgivings about the Liverpool job are based purely on the uncertainty 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 Fulham boss is aware that the current regime are able to offer him only “limited” security and certainly not beyond their own tenure on Merseyside. A change of ownership would immediately put his future in doubt.
Nevertheless, Hodgson is willing to take up the reins at Anfield should England progress into the knockout stages of the World Cup, which would likely end any uncertainty over Capello's own position.
Hodgson is confident he can work with the resources at his disposal better than many other big-name managers and recognises that he will have to wheel and deal in the transfer market and work on a restricted budget given the club's £350 million debts.
Meanwhile, Fulham have already begun to explore the possibility of lining up a replacement for Hodgson.
Goal.com UK can also confirm that Sven-Goran Eriksson is the London club’s top target, followed by Mark Hughes.
Both managers have worked with Fulham chief executive Alistair Macintosh when he held a similar role at Manchester City.
Eriksson, whose contract as Ivory Coast boss expires at the end of the World Cup, is believed to have had a very good working relationship with Macintosh at Eastlands before both men lost their jobs in the summer of 2008.