Qatar was awarded the right to host the competition in 2010, but that decision has attracted widespread criticism due to the searing Middle Eastern temperatures in June and July, when the World Cup is traditionally held.
Moving the competition to Qatar's cooler months has been widely suggested, although there would be a severe impact on domestic leagues around the world.
Qatar's bidding group remain confident of staging the tournament during its standard timeframe, but a FIFA task force has revealed they are now close to proposing new dates.
"We are getting closer to narrowing the dates for the FIFA World Cup to two options - January/February 2022 or November/December 2022 - but FIFA has also been asked to consider May 2022," said Valcke.
"We will summarise what we've heard today and provide feedback to all parties in order for them to prepare for the next meeting as we progress towards a final decision."
The task force has been set up by the FIFA Executive Committee to assess the international calendar from 2018 to 2024, with the World Cup in Qatar its hottest topic.
