That list shows the many different approaches the Football Association has previously used in identifying the right candidate -- from experienced foreign coach (Capello) through respected English club manager (McClaren) to passionate former player (Keegan).
Each time the demands of a job, which currently pays 3.5 million pounds ($4.68 million) per year but which many view as impossibly difficult, have defeated football's finest minds.
It is half a century since the country which gave soccer to the world last won anything -- the 1966 World Cup.
While major nations such as Germany, France and Spain have been winning trophies in the last two decades, the best achievements England fans have celebrated were semi-final appearances at the 1990 World Cup and at Euro 96.
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There appears no obvious successor to Hodgson, who has been pilloried in the British media after England's embarrassing second-round defeat by Iceland on Monday which came 50 years after their only international success at the 1966 World Cup.
The search will be conducted by Dan Ashworth, the FA's technical director, alongside chief executive Martin Glenn and Dave Reddin, the head of performance services.
England Under-21 coach Gareth Southgate, who recently oversaw an England victory in last month's Toulon tournament, is the early bookmakers' favourite.
But the 57-capped former England centre-half is far from a shoo-in and his candidacy was immediately knocked down by respected former Tottenham Hotspur manager Harry Redknapp, who was pipped by Hodgson to the job in 2012.
"Why should he [Southgate] get it in front of [Hull manager] Steve Bruce and [Sunderland manager] Sam Allardyce, who are proven managers?" said Redknapp, who denied that Southgate's familiarity with the FA and the "English system" was an advantage.
"Knows what system? The losing system? He knows the losing formula? I like Gareth Southgate, he's a great lad, but what's he done?"
Another former international, the TV pundit Alan Shearer, was quick to put himself forward although, with little coaching experience -- apart from a short spell at Newcastle in 2009 -- he would be an outside choice.
Frenchman Arsene Wenger, who is widely respected in the English game after 20 years at Arsenal, would be a popular choice should the FA drop its current policy of appointing an English candidate,
Wenger's credentials were championed by former England international Teddy Sheringham on Tuesday.
''It's time England turned to Arsene Wenger," wrote Sheringham in a blog for a bookmaker.
"England have strength, passion, desire, hunger, and bullishness. They are strong-minded and resilient. But England need structure. They need guile and finesse. If you look at the way that Arsenal play, they have a structure to the team.''
In the past Wenger has always distanced himself from the job, but is under pressure at Arsenal after again failing to win the Premier League for the Gunners.
If Wenger could be persuaded to take the job, he would join two other foreign coaches currently bringing success to the national teams in England's other two major sports: Australians Eddie Jones in rugby union and Trevor Bayliss in cricket.
But the FA is aware that to put a foreign-born coach in charge of England's football team would undermine its argument with the all-powerful Premier League about the need for teams to field more English players.
(Reporting by Neil Robinson)
