The Premier League reiterated its strong opposition in a statement but its stance was undermined by Sir Dave Richards, who admitted the tournament cannot be staged in the summer due to the heat.
Richards, who is due to step down as Premier League chairman, admitted that a compromise was likely to be reached in the build-up to the competition.
I think they will play at a time that is proper for football but they will have to speak to the leagues in Europe," he told Sky Sports News from the Securing Sport conference in Qatar.
"They will have to agree proper times when we can start and finish.
"At the moment it has a tremendous amount of implications for Europe. For us, at this minute, the answer is no.
"But, if we take a proper view, we have to find a way to have a winter spell where we don't play and I think common sense will prevail.
"We've got Fifa now saying that medical people are saying that they can't play in Qatar in the summer because of the heat, which is probably right.
"I think over the next few years, things will change and they will come to a compromise."
Fifa general secretary Jerome Valcke admitted earlier this month that there was a case for moving the World Cup, with the international calendar yet to be drawn up for football beyond 2018.
And yesterday Jim Boyce, Britain's Fifa vice-president, indicated he also supported a winter switch for the tournament after Uefa president Michel Platini's call for the World Cup to be played in Europe's winter when it heads to the Gulf.
"Many other countries already have a winter break so for them it should not be too problematic," he said.
"England is probably the main country where there is no winter break but I believe that even there if they are given enough notice then for just one season it should be possible.
"People I know who live in Qatar say it would be very uncomfortable for the fans. There is also a medical and health concern for both players and spectators and if it is going to be safer to play it in January instead of July then I would be in favour of that."
However, a spokesman for the Premier League insisted they were still opposed to any winter competition which would disrupt the domestic game's schedule.
"The Premier League's view remains unchanged," he said.
"We are opposed to the concept of a winter World Cup for very obvious practical reasons that would impact on all of European domestic football."
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