Harry Redknapp remains the overwhelming favourite to be appointed as Fabio Capello's successor, but alternative options are being discussed.
Hodgson's vast experience makes him an obvious candidate, with the 64-year-old having been involved in coaching for 30 years.
The vast majority of his management career has been spent at the helm of club sides, but he has also worked with Switzerland, the United Arab Emirates and Finland at international level.
He has been billed as England manager material in the recent past, but Hodgson is reluctant to discuss any possible claims he has to the post while speculation continues to rage.
"I don't think it's right to say whether you are interested or not," he told Sky Sports News HD. "The FA need to decide who they think are the right people. They need to decide what candidates are out there.
"It seems at the moment that Harry is receiving all of the backing from virtually all the quarters, but it's up to them to decide what they want to do.
"I don't think it's right for people like myself to say 'I'm interested' or 'I'm not interested' because I have no idea what the FA have got in mind or what they want to do."
Pressed on whether he would be interested in the role if it was offered to him, Hodgson added: "It's hypothetical. When and if that day comes, then I will be able to take stock of the situation and make a decision.
"I think it's arrogant to rule yourself in jobs or rule yourself out of jobs when there is no indication that anyone is going to want you in the first place."
Hodgson's contractual situation at West Brom means he could be lured away from The Hawthorns with the minimum of fuss, but he says he is happy to continue testing himself on short-term deals at club level.
"I think it's right to keep one's options open," he said.
"The situation we have here is a very good one and I enjoy my work here. Hopefully people appreciate the work I try to do, that's fine. I am happy to keep my options open but I haven't kept them open for any particular reason. I certainly haven't kept them open in relation to the England job.
"Basically speaking, I shall see what happens between now and the end of the season and hopefully be able to make a decision on my future a little bit later on.
"One would hope anyway that the Football Association will decide, as I have heard them say, that they want what they consider to be the right man for the job. I don't think whether people happen to be in or out of contract will necessarily affect that situation."
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