A summer World Cup in Qatar in 2022 would be "impossible", says the FA's new chairman Greg Dyke.
Mr Dyke says FIFA has two choices - to move the World Cup to a cooler part of the year or give the tournament to another country.
But he believes a winter World Cup is more likely.
It is the first time the FA has taken a formal position on the controversial issue, although Mr Dyke's predecessor David Bernstein said in June that any plans to move the World Cup to the winter were "fundamentally flawed".
The latest statement could lead to some differences with the Premier League, whose chief executive Richard Scudamore strongly opposes any move to change the World Cup to the winter.
Mr Scudamore says such a move would cause disruption to domestic club competitions.
Mr Dyke said: "I don't know how many people have been to Qatar in June. I have. The one thing I can tell you is you can't play a football tournament in Qatar in June.
"Even if all the stadia are air-conditioned - which seems a bit strange in terms of the green policy - it would be impossible for the fans just to go out there, wander around in that sort of heat.
"The FA's position will be you can't play it in summer in Qatar.
"FIFA therefore has two choices; you either move it in time or to another location.
"I suspect either ends up in some sort of litigation, but then someone should have worked that out in 2010 when it was awarded.
"It is then up to FIFA to decide whether to move it from Qatar or move it into autumn or winter. That's what the discussions will be over the next few months.
"I understand the reaction of the Premier League to not want to move it. I have some sympathy with them.
"They didn't have to choose to give it to Qatar in the summer but that's where it is. It will either have to be moved out of the summer or another location. I suspect the former is more likely than the latter."