Allardyce has a long history of managing in England but has never had a high-profile job like coaching England. He'll leave Sunderland less than a year after taking over the Black Cats and rescuing them from sure relegation.
English FA chief executive Martin Glenn, vice chairman David Gill and technical director Dan Ashworth headed the search, and Glenn confirmed on Wednesday that the 12-man FA board will meet to go over the search on Thursday.
"It's been three weeks since the hunt started and we're making good progress," said Glenn. "We're clear about what we're looking for and we've interviewed a handful of people. We're after the best man for the job and we've got to get that right. We've got to have covered all of the alternatives before we make our decision. Everyone we have spoken to about the job has been massively enthusiastic. We don't want a short-term solution for a couple of years, we want someone to work alongside the development teams in terms of giving them a ladder."
It's easy for Glenn to say the FA doesn't want a short-term solution, but that flies in the face of the results-oriented nature of the international game. Hodgson kept his job after England didn't make it past the group stage at the 2014 World Cup but he quit immediately after England departed Euro 2016 following a loss to Iceland.
England's early exit was disappointing because it has some good young players such as the Tottenham trio Harry Kane, Dele Alli and Eric Dier. There have been signs the soccer young English players are playing is getting better, as our colleague Paul Gardner has pointed out.
England is playing at the UEFA Under-19 Championship in Germany and enters Thursday's semifinal against Italy having won all three games, including a 2-1 victory against the highly regarded French team.
Allardyce has the reputation of being a fix-it man but he outlined big plans for the national team program when he first applied for the England job a decade ago.
Steve McClaren, who beat out Allardyce for the job in 2006, lasted two years, Italian Fabio Capello four years and Hodgson most recently four years.
It will be interesting to see how long Allardyce gets.