As reported in the Daventry Express, Sam Chambers, coach of Weedon Bec Primary School, sent his CV to the FA after England crashed out of Euro 2016.
"I feel like the perfect candidate as I have guided my school... to an unbeaten 2015-16 season," he wrote.
Ladbrokes has made him a 1,000/1 outsider for the job.
Roy Hodgson stood down as England manager after the shock 2-1 defeat to Iceland last week.
Jessica Bridge from the bookmaker said: "Stranger things have happened in the last 12 months, like Leicester City winning the Premier League, so it's not out of the realms of possibility.
"Sam enters the record books as one of the greatest sporting underdogs of all time."
Mr Chambers, who describes himself as a "sports enthusiast", faces stiff competition from current favourites Jurgen Klinsmann and Sam Allardyce, but says he has the passion to be a success in the job.
"I, along with millions across the nation, saw our beloved team fall to the minnows that are Iceland," he wrote in his covering letter to the FA.
"It is my intention, should I be given the opportunity, to re-kindle the enthusiasm of the nation for the round-ball game."
Elaborating on his school's impressive season, Mr Chambers added he had guided his side to an unbeaten campaign - even though they faced "mighty teams such as Woodford Halse CE Primary Academy".
He ends the letter with an optimistic "I look forward to hearing from you all!"
The FA is yet to comment on Mr Chambers' application.
Earlier this year, a seven-year-old boy failed in his quest to become Inverness Caledonian Thistle's new manager, despite a pledge that his headmaster would probably let him leave school early "for important matches and training".

Healy's tour may be over after he sustained suspected ankle ligament damage against Western Force.
Team: London Irish
Position: Prop
Age: 24
Height: 1.86m
Weight: 118kg
England caps: 18
"Cian has had an X-ray and, while his left ankle is not broken, he will be assessed further," said Lions coach Warren Gatland.
"In the meantime we need to get Alex over here as soon as possible."
Healy, 25, twisted his left leg in the 37th minute of the Lions' 69-17 win on Wednesday and had to be taken off on a stretcher in Perth.
The Ireland international has also been cited for allegedly biting Western Force scrum-half Brett Sheehan.
Corbisiero, 24, was part of the England squad currently in Argentina for the two-Test tour, but has been released immediately to join Gatland's team.
The Lions play Queensland Reds in the third match of their tour on Saturday.
"We're delighted for Alex," said England head coach Stuart Lancaster. "It's very pleasing for him after he missed the Six Nations through injury and he goes with our full support and blessing."
England have no plans to add a replacement to their squad in Argentina.
The Red Rose face the Pumas on Saturday (20:10 BST) in the first Test, before the sides meet again in the second Test on 15 June.
The coach of a primary school football team has applied for the England job, saying he is the "perfect candidate" to succeed Roy Hodgson.
[NEXT_CONCEPT]
England prop Alex Corbisiero has been called up to the British and Irish Lions squad to provide cover for the injured Cian Healy.