The Swede will step down after the World Cup finals in Germany this summer.
FA chief executive Brian Barwick (pictured right), international committee chairman Noel White and Premier League chairman Dave Richards are the three men who have been appointed to find a new boss.
BBC Sport rounds up the latest news and speculation surrounding the vacant England job.
More revelations about the FA's plans in the Daily Express.
This time reporter Harry Harris claims that Alan Curbishley paired with Stuart Pearce is the preferred FA choice. The governing body has its concerns about Sam Allardyce, it appears.
The Express has championed the cause of Curbishley, who is a columnist for the paper, but Harris writes that his inside information has come from a "leading Premiership chairman".
Meanwhile Charlton chairman Richard Murray says: "As a club our position remains the same as ever - we do not want him to go, but if it is offered to him, and he wants to take it, we will not stand in his way."
Send us your comments on who should be England coach and why using the form below and we will post a selection here. I want the manager to be English and whoever they appoint I hope it's not a duo like Pearce and Curbishley working together. That will not work - the next manager need to be in sole charge.
ed brand, united states
I would love to see Martin O'Neill put in charge with Alan Shearer as his assistant, that would be pure class and dedication.
Darren Woodacre, England
Stuart Pearce without doubt. He epitomises England and with the players we currently have would make England roar once again!
Jon Darcey, England
Guus Hiddink of the Netherlands, succesfull with all nationalities, reader of the game, well done with South Korea and now with the Socceroos.
B J Karreman, RSA
The FA should decide whether trophies or an English manager is important. There is no one to match the credentials of Luis Solari or Guus Hiddink at this moment to steer the most talented England team.
Suren, India
Let's say Guus Hiddink. What he did for Korea was excellent and I believe he'll be the one to lead England to the World Cup trophy.
nicky, Nottingham, England
What about Guus Hiddink as manager and Stuart Pearce as coach - experience of winning at international level combined with English passion - the Dream Team!
Phil, Bristol, England
I think it should be O'Neill. Everywhere he has been he has done extremely well, and although he's not English he still knows what the job is all about. He would be better than five minute wonders such as Stuart Pearce and the - in my opinion - club specialist Sam Allardyce.
Ronnie, Scotland
Big Sam would be a revelation - he'd certainly light a fuse under some of those players who think they can just stroll through a game; he might even get Beckham playing! (Real Madrid can't).
Fred Dixon, Australia
Martin O'Neill has the motivational skills that are vital, as well as the tactical know how. The players are all great - they just need the right organisation and methods. O'Neill, with support from Psycho for me. Definitely not Curbishley.
Glenn Beckett, England
People have said Alan Curbishley has no experience with a top side, but how will he gain that experience, if he doesn't get the chance? Now his chance is with England and he would do a cracking job as he's dedicated to his job.
William , England
Big Sam. He can get blood out of a stone. Look at Bolton with no money. He has the carisma and will not be bullied by the press.
Keith, Australia
Sick of seeing Ronald Koeman beating England and English teams as a player and manager. Why has nobody mentioned him
steve robson, Brasil
The point is none of the English candidates have world class experience. Lets not have bias, cloud our judgement. Look at what Hiddink et al have done with other international sides
andy sykes, UK
Why is everyone overlooking Steve McClaren? He's the only one of the English mangers that are in contention with Champions League experience whilst at Man Utd, he won Boro's first ever trophy, got them into Europe and knows the England squad inside out with his assisting role for England
John Webb, England
One name everybody is overlooking - Steve Coppell! Excellent player, excellent manager, experienced, why not
Chris Leonard, Canada
Why is no one considering Peter taylor, the Under 21 manager? He has plenty of European experience and has been successful at that international level.
Brian, England
Why is everyone in love with Big Sam? Route One, aggressive football is not what wins World Cups. Martin O'Neill is the man we all want. We have the best set of English players in generations, please don't mess it up FA.
Graeme, England
Big Sam has a big English heart, and I would go as far as to say he is the football fans' first choice. He has done an excellent job at Bolton, and has the strength of character to steer our national side to great achievements.
Roy Blendell, England
How about Roy Hodgson? Proven international success on a smaller scale with Switzerland, plus experience at top European club level. We need to start thinking about playing with a style that can compete with the top teams, and that requires a manager with international credientials. Passion is very important, but passion won't win trophies. Every other country tries just as hard as England!
Simon, Derby, UK
It's got to be Hiddink. His claim stands out a mile over anybody else's. I like the idea of teaming him up with Pearce though, that should ensure that there's some longevity about the new management team.
RJ, England
What about Alan Pardew. He is passionate about the English game and has done wonders at West Ham this season. Sorry to be so Hammers biased but I think Trevor Brooking should be the figure head with the other candidates whoever they should be (Curbishly, Pearce et al) as the coaches
Martin Haley, UK
Nobody has put Luther Blissett into the pot, I think he would do a great job. He was head coach for us (York) for a couple of games and he proved he can do the job. He was also Graham Taylor's number 2 for a while, I think he could do as good a job as any man.
Carl Hodgson, England
For me the right man for the English job is Glenn Hoddle. In 1998 Hoddle began to get England playing good football once again. I will always remember the gritty English midfield manned by Batty and Ince. Please forgive him and give him another chance.
Allan Amponsah, Ghana
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