Hodgson has previously been linked with the England job himself.
Liverpool face Tottenham at White Hart Lane on Sunday.
Hodgson said: “Harry’s got the attributes to do the job, no doubt about it.
“We’ll have to wait and see but it would surprise me if the FA don’t choose at Englishman to take over from Fabio should he indeed decide to step down after the European Championship in 2012.
“Public opinion seems to favour an Englishman being in charge again and Harry will be a major candidate because of what he’s achieved.
“It doesn’t surprise me that Harry has said he wants it because it’s the pinnacle of everyone’s ambition.”
Hodgson added: “Harry’s doing very well at the moment and the thing about the England job is that it tends to be the person having the best run when the job becomes available who is flavour of the month.
“I remember Alan Curbishley being a major candidate when Sven Goran Eriksson left, but he hasn’t had a job in football management since leaving West Ham.
“That’s the nature of the job we’re in. I’ve had spells in the past when people have said ‘what about you?’
“So I suppose we will have to wait until the day when the England job becomes available to see who is the brightest kid on the block.”
