With temperatures in the region of 50C during the summer months, the former director general of the BBC has backed plans to move the tournament to a cooler period
Unless the tournament is changed to the country's winter months, players face the prospect of competing in temperatures which can reach 50C.
Fifa president Sepp Blatter has previously admitted that it is "not rational" to host the 2022 World Cup throughout June and July in Qatar, though Premier League chief executive Richard Scudamore is against moving the tournament to the winter.
"Even if all the stadia are air-conditioned, I think it will be impossible for the fans," told reporters Dyke.
"Just go out there and wander around in that sort of heat. I just don't think it's possible.
"My position, and I suspect the FA's position, will be: 'You can't play it in the summer'."
The 66-year-old, who visited Qatar in June, added: "Fifa have therefore got two choices. They can move it either time-wise or to another location. I suspect either will end up in some sort of litigation. But then someone should have worked that out in 2010 when it was awarded.
"I understand the reaction of the Premier League in not wanting to move it, and I have some sympathy with them.
"We didn't have to choose to give it to Qatar in the summer. But that's where it is, and I think it will either have to be moved out of the summer or moved to another location.
"I suspect that the former is more likely than the latter."
The Premier League, however, believes any rescheduling would impact three seasons - 2021-22 and a campaign either side - as well as broadcasting and player contracts, a scenario Scudamore previously branded "chaos"