UEFA President Michel Platini is a staunch opponent of playing the World Cup in the expected 40 degrees celsius heat of June or July and on Saturday he called again for the finals to be switched to the winter months.
Valcke stepped into the seemingly never-ending debate at a media briefing following the International Board meeting in the Scottish capital where he said staging the Cup during the winter was a possibility.
His remarks were significant because it was the first time FIFA has indicated it could instigate a change based on medical evidence.
"Qatar has to tell us 'we want to move the World Cup from summer to winter'," Valcke said.
"I can tell you there is no working group within FIFA thinking and working on what it means to move the World Cup from summer to winter for the time being.
"The international calendar has been agreed for 2015-2018, meaning that we kept open all potential for period 2019 to 2022. We have time.
"FIFA has never said 'never', we have just said 'we are waiting for Qatar to officially ask FIFA to look at the potential to move the World Cup from summer to winter' and that has not happened yet.
"Qatar is perfectly aware and 2014 is not the deadline it can be even in 2015.
"The most important thing is to make sure work with all stakeholders and make sure there is full agreement with all parties, leagues, clubs and we would have to find eight weeks in the mid-season to play the World Cup."
Valcke said FIFA's executive committee would make a unilateral decision only if there were strong medical evidence in favour of a change.
"The FIFA executive committee has the power to make decisions and if at the executive committee this issue starts to be a real point for discussion then why not, and then again maybe the committee will say based on medical reports, or whatever, we really have to look at playing the World Cup not in summer but in winter.
"I am not saying that the case is closed but what I'm saying is as long as we have not fixed the international calendar all alternatives are open.
"I think it would be good to have a final decision about when this World Cup will be played and have an agreement between all the football family but it's in 2022, nine years and we have two World Cups to organise in Brazil and Russia so there is some time."
CONCACAF President Jeffrey Webb said earlier on Saturday he was opposed to changing the timing from summer to winter.
"Historically the World Cup is always played in June and July and I would definitely like the World Cup to be played in June, we accepted it. We went through a long process regarding that," he said.
"We all knew the World Cup was going to be played in June and July and as far as I am concerned, that's accepted."
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