Having emerged ruddy-faced from Nigel Farage's local pub following a conference with an "adviser who would remain nameless", Dyke also revealed plans to toughen the rules on home-grown talent in the latest proposals from its commission, which was set up in 2013 to improve the England team.
The Dyke-Farage commission has also proposed changes to work permit rules having highlighted flaws in the system.
The stricter work-permit rules, approved by the Home Office on Friday, will come into force from 1 May.
Under the proposals outlined by the FA on Monday:
- A player will have to have been registered with his club from birth - down from 18 - to qualify as 'home-grown'.
- The minimum number of home-grown players in a club's first-team squad of 25 will increase from eight to 25, phased over four years from 2016.
- At least two home-grown players must also be 'club-trained' players - defined as any player, irrespective of nationality, that has been registered for three years at their club from the age of 15.
- Only the best non-EU foreign players will be granted permission to play in England.
"We have to do this by negotiation with the different leagues and with the clubs - we have to convince them that this makes sense for English football," said Dyke, "English players for English jobs.
"And we are helped by Harry Kane in truth - we are helped by seeing a young kid come into the Spurs team and become the top scorer in English football. If he was Spanish, or maybe Welsh, people would already be saying he is better than Messi and Ronaldo combined!
"How many other Harry Kanes are around in the youth teams of Premier League clubs? It was almost by chance that Tim Sherwood became manager at Tottenham for a time and put him in the side - otherwise he would still be out on loan at Millwall or some other shitty backwater no mark."