It was a statement that was met with both humour and disbelief in equal measure. After all, the Three Lions have reached just one semi-final since they lifted the Jules Rimet Trophy back in 1966.
What is more, as Dyke pointed out himself, English footballers make up just 32% of the player representation in the Premier League.
However, despite all that, Dyke has found an ally in Aston Villa's Under-21 player Lewis Kinsella, who has told Sports Mole that if the right system alterations are made, there is enough "talent" coming through for England to challenge in nine years' time.
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"That is a realistic target. There is good and young English talent coming through. There is a lot - players like Nathaniel Chalobah, Alex Pritchard and Tom Carroll - these are players that are at top teams but they are just not getting the chance [at club level]. They are showing how good they are at Under-21 level, though," said Kinsella.
"[Being made to have at least three English players in a squad] is a brilliant idea. It would give the younger players a chance to come through and have new experiences, which will develop them as players."
Kinsella, 18, spent the first eight years of his trainee career with Arsenal, whose manager Arsene Wenger is famed for giving youth the opportunity to flourish. Yet, where English personnel is concerned, only Ashley Cole, Jack Wilshere and Kieran Gibbs have made notable impacts on the senior side at the Emirates Stadium in recent memory.
While his ability was honed under the watchful eye of Wenger's coaching staff at the Gunners' Hertfordshire training base, Kinsella believes that he has a greater chance of realising both his Premier League and international ambitions at Villa Park.
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"Villa give you more opportunity than other clubs. Our philosophy at Villa is that we will work hard as a team. You can play exciting football, but firstly you've got to put the effort in. Other teams might be more technical, but we are still a technical team. The main thing is that the coaches [at Villa] are willing to give us a chance," claimed the youngster.
"[Arsenal] teach you a good way of how to play football - how to keep the ball and move it quickly. I enjoyed my time there but they signed a lot of foreign players at my age and I had to leave. Villa seem to give English youngsters more of a chance. Arsenal do bring through a lot of English and British youngsters, just not at the club. If you look at Jay Emmanuel-Thomas, Sanchez Watt, Benik Afobe - most of them end up out on loan and then leaving permanently. They just become a professional footballer somewhere else."
The left-back's opinion on Villa's academy is backed up by their past results. They are a competitive force domestically, but have also proved themselves to be one of the strongest squads in Europe by winning the NextGen Series at the expense of Chelsea last season.
Due to insufficient funding, the tournament has been shelved for the next 12 months at least. It has been replaced by a UEFA Youth League, but only Europe's major clubs are permitted to compete. It means that Kinsella, as well as a host of English youngsters will miss out on some valuable experience, according to the Watford-born defender.
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"The NextGen is massive. That is the best tournament that I have played. When I was at Arsenal we used to go on tours to Spain, Portugal, France, Belgium and Holland playing all sorts of teams, but the NextGen was more like a Champions League and much more competitive," he revealed.
"This season they've changed it so only the top four teams [from England] can enter it. I don't think that's fair because there will so many young players missing out on the experience of playing teams from abroad. It's a totally different game when you play against overseas footballers.
"Even at the beginning or end of a season, English teams should play clubs from abroad. It's so beneficial. Technically [foreign teams] are very good. We played Marseille a year before last and every time we put in a tackle, they'd fall to the ground, diving. They'd do anything that they possibly could to win. You have to be careful with your tackles and that you don't lash out because if they overreact, you could end up getting sent off. You've got to be more clever.
"If you pressure them they don't like it, whereas if you are playing against the likes of Manchester United, Arsenal or Liverpool, they'll push you back and hit you hard. They won't try to get you sent off like they sometimes do abroad. If they see that a certain player has got an angry streak in him, like Wayne Rooney and Cristiano Ronaldo [in the 2006 World Cup], they realised Rooney was easily wound up and they ended up getting him sent off."
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On a more personal level, Kinsella, who is yet to turn out for Villa's first team, is hoping that in the future he will be granted permission to follow in the footsteps of current England internationals Frank Lampard, Danny Welbeck and Daniel Sturridge, all of whom had loan spells earlier in their career.
"I'm just trying to concentrate on having a good season and staying free from injury and then we will see if I get a new contract, hopefully I do. I'd like to go and play first-team football somewhere, but at the moment I've got to get my head down and play well for the Under-21s," explained Kinsella.
"Every league is different - if you go and play in League Two, it's a lot more physical and a lot more direct. Some teams play football there and some don't. Mainly, it's much more physical, which would make me a stronger player. I'd like to go on loan, I think it would be a good experience."