NICE: Wanted someone to turn around the fortunes of soccer's most consistently underperforming international team.

England was beginning its search for a new coach Tuesday after Roy Hodgson's departure following the team's latest embarrassing exit from a major tournament, this time at the hands of tiny Iceland at the European Championship.

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And there aren't too many obvious candidates for a role often labeled "The Impossible Job."

Gareth Southgate, the coach of England's under-21 team, is an early if underwhelming favorite to succeed Hodgson. There's talk of Sam Allardyce, Alan Pardew and Eddie Howe — all current Premier League managers and all from different parts of the age spectrum.

And if experience is what the FA hierarchy after, they could do worse than try to entice Arsene Wenger.

Criticism of the Frenchman is growing among Arsenal's fan base after 20 years at the London club, and Wenger could be tempted by a first international job, perhaps the final one of his career.

The FA will look to have its new man in place well in advance of England's next match, a World Cup qualifier away to Slovakia on September 4.