There is a dearth of options to succeed the 68-year-old, with Dyke - who leaves the FA next month - appearing relieved not to be involved in those discussions.

"It's got to be somebody who really knows English football," he said, as reported by The Guardian.

"But there are loads of them now, more of them than there are English.

"You need someone who knows about English football. But Martin (Glenn, FA chief executive) made clear you go for the best person. The harder question is why anybody would want it?"

It was a remarkable comment from the man who has been FA chairman for three years and set the well-documented challenge to win the World Cup six years from now in Qatar.

The gravity of the decision led FA chief executive Glenn to suggest on Tuesday it could take as long as a year to name a permanent successor, saying England U-21s manager Southgate would be a "pretty obvious" interim solution.

However, it was widely reported yesterday evening that he has no interest in succeeding Hodgson, nor has he been contacted by the FA.

Those reports saw the odds on him becoming England manager lengthen, although the man who led the U-21s to Toulon Tournament glory last month remains favourite ahead of ex-England manager Glenn Hoddle, United States boss Jurgen Klinsmann and Sunderland's Sam Allardyce.

The latter would be former FA chairman David Bernstein's choice if they plumped for a home-grown boss.

"I'm not saying we should have an English manager," he told the Daily Telegraph. "But, of the English managers, I actually would go for Sam Allardyce.

"He's a very powerful character. I think he's got the personality, the strength, he's a good technical manager, he's very experienced and he's someone who perhaps could imbue confidence.

"Because, clearly among other things, there's a psychological problem with our players, where they seem to get to a stage with international football where they just can't cope, and that's manifest time and time again, year after year, in individual errors which you just wouldn't expect from players.

"You had Steven Gerrard's error at the World Cup last time which cost us, you've got goalkeeping errors.

"A general psychological malaise seems to overcome them. They seem to freeze.

"Someone like Sam Allardyce may have that personality and strength to do a little bit of what has happened to the England rugby team."

Bernstein was FA chairman when Hodgson was named manager in 2012, but despite back-to-back early exits from major tournaments has no regrets.

"I believe we ended up with the best candidate, someone who's extremely credible, who had taken Switzerland to third in the world, who had international experience therefore, and who had a good club record," he said.

"I'd in no way go back on the exercise that we did and I'm very sorry and surprised the way it's finished."