The Football Association are meeting today to draw up a shortlist for the vacant position after Capello resigned on Wednesday.
Tottenham's Harry Redknapp is the overwhelming favourite for the role but, with the FA keen to appoint an English or British manager, Hodgson's name is also up there.
Newcastle's Alan Pardew and West Ham's Sam Allardyce have ruled themselves out of contention, but Hodgson - who was strongly fancied to succeed Capello following the 2010 World Cup - preferred to keep his options open.
"I don't think it's right to say whether you're interested or not,'' he said. "The FA need to decide who they think are the right people and to decide what candidates are out there.
"Harry's receiving all the backing from virtually all quarters, but it's up to them to decide what they want to do and I don't think it's right for people like myself to say: 'I'm interested or I'm not interested' in the job because I've no idea what the FA have got in mind and what they want to do.''
On what he would do if he was offered the job, he replied: "That's hypothetical. When and if that day comes then I'll be able to take stock of the situation and make a decision, but I think it's arrogant to rule yourself in for jobs or rule yourself out for jobs when there's no indication that anyone's going to want you in the first place.''
Hodgson is only under contract at The Hawthorns until the end of the season - and seems quite content with that scenario.
"I think it's right to keep one's options open,'' he said. "The situation I have here's a very good one. I enjoy my work here and hopefully people appreciate the work I'm trying to do.
"I'm happy to keep my options open but I haven't kept them open for any particular reason, and I certainly haven't kept them open in relation to the England job.
"I've heard the FA say they want the best man for the job and I don't think whether people happen to be in or out of contract would necessarily affect that situation.''