Tottenham Hotspur manager Harry Redknapp is believed to be the current frontrunner to replace the Italian when he leaves his post following the conclusion of England's 2012 campaign.
However, it is understood that Hodgson, who has just been appointed as Roberto Di Matteo's replacement at West Brom following a disappointing spell at Liverpool, is also in contention.
The FA is insistent it is very committed to Capello while he remains in position and it may be some time before a definitive shortlist of replacements is drawn up. Indeed, the subject was not on the agenda in the first board meeting held by new FA chairman David Bernstein on Thursday.
But Hodgson is regarded within the FA as a safe pair of hands and of course fits the criteria of being English, which the FA is keen to fulfil if possible. Sunderland's Steve Bruce has also been earmarked as a possible contender.
Former Aston Villa manager Martin O'Neill, and indeed his replacement Gerard Houllier, are also under consideration, but Redknapp remains the favourite after a week that saw him mastermind a 1-0 victory against Milan in San Siro.
An FA insider told ESPNsoccernet: "Everyone is assuming the FA have made up their minds. This is a completely incorrect assumption. There are a lot of factors the FA need to consider, and they may not be as clear cut as everyone might assume.
"The FA has a new chairman, and much will depend on his opinion, his outlook, and how he wants to go about looking at the criteria to find the next England manager, whenever that time comes."
Frank Lampard believes Harry Redknapp would be an "outstanding'' England manager. Chelsea midfielder Lampard, who is also Redknapp's nephew, told BBC Sport: "It's for him and the FA to decide but it'd be nice if it were an English manager.
"At the moment, Harry's doing a fantastic job at Spurs and if he has an opportunity to manage England, I'm sure he'd be an outstanding manager. But, at the moment, we have to play for Capello and we have to win something.
"Since the World Cup, we've had good and not so good results. We haven't turned the corner yet. That is a process and takes time. When we reach the European Championships and do better than we did at the World Cup then we can say we have.''
Meanwhile, it is understood that Bernstein's first board meeting produced an agreement in principle that two independent board members will be appointed by the FA - a concession to pressure from the Government.
It is understood that the issue was given cautious approval by the board. The biggest problem is winning over the full FA Council, which is generally opposed to radical change.