The news follows an approach from FA chairman David Bernstein to West Bromwich Albion chairman Jeremy Peace.
No approach has been made to Tottenham boss Harry Redknapp, who had been viewed as the favourite to succeed Fabio Capello.
Hodgson has previously said: "It would be an honour of course if ever the offer came my way, because it's the pinnacle of success in a way and certainly of coaching success if you are ever invited to manage your own country."
Asked if he would take the job if offered it, Hodgson said: "Of course, I think that anyone would."
But what have other people made of the news? Here are some of the views...
Eurosport expert Jim White: "Roy's the FA's man because he's an FA man."
Mark Perryman of the England Supporters Club: "It's almost inconceivable they haven't approached Redknapp. I think the fans and the broader sporting public have a right to know what the situation is with Redknapp. I don't think there will be a great wave of excitement about Hodgson but given that (Jose) Mourinho or (Pep) Guardiola are not likely to take the job..."
Stan Collymore: “I’d be happy-ish to have Roy manage England. Just worried that fans, press will turn quickly...”
Henry Winter of the Daily Telegraph: "Stand up & be counted time: I'm backing Hodgson. He doesn't have Redknapp's popularity with players/fans but he knows international football."
Dave Kidd of the People: "The FA are prepared for a public outcry but are convinced Hodgson ticks all boxes. As am I."
Sam Wallace of the Independent: “Reliably informed this isn't a negotiating tactic on the FA's part. Roy Hodgson is their No.1 choice to be the next England manager.”
Matt Law of the Daily Express: "Hodgson struggled when he worked in a more solitary capacity at Blackburn and Liverpool. England job can be a lonely one."
Oliver Kay of The Times: “Looking forward to seeing who's the first England player to tweet "Always admired Roy Hodgson”.
Gordon Farquhar of Radio Five Live: "So the FA break cover and go for Roy Hodgson not Harry Redknapp. It will be a done deal. They have kept a very tight lid on the process."
Sean Ingle of the Guardian: "What chance Roy Hodgson attempting to do an Otto Rehhagel at Euro 2012? (ie seven players sitting deep, trying to win every game 1-0)."
Matt Dickinson of The Times: "First thought this morning is sympathy for Redknapp. Will brush off his disappointment in public but bound to hurt."
Matt Lawton of the Daily Mail: "If people feel FA have gone for second best when best candidate was available they are going to question it."
Paul Hayward of the Daily Telegraph: "Can see why the FA are courting Hodgson, with Burton etc in mind. He has a fine record."
Rob Harris of the Press Association: "FA wouldn't have to pay compensation to West Brom to hire Hodgson since his contract expires at the end of the season."
Jonathan Wilson of The Blizzard: "Roy Hodgson has a terrible habit of getting good jobs in bad circumstances."
What do you think of England's talks with Hodgson - is he the right man? Would you prefer Harry Redknapp or another candidate?
Post your views below...