FIFA is considering moving its tournament from the usual June-July period to avoid the scorching summer heat in Qatar.
FIFA President Sepp Blatter has suggested November, while UEFA President Michel Platini prefers a January start. A January World Cup would conflict with the lead-in to the 2022 Winter Olympics in February.
"That's why we have to sit at the table and discuss: 'Sepp, what do we do? How do we go?'" Fasel said.
Fasel believes there is plenty of time for winter sports to contribute to FIFA's consultation, which is expected to run through 2015.
A spring option in April-May 2022 has been suggested by Karl-Heinz Rummenigge, head of the European clubs' association.
"For the moment I keep cool," Fasel said. "We will see what really will be the decision in FIFA, how Qatar will react and which position there will be."
Skiing's governing body, which has long cautioned FIFA against moving into the traditional winter sports calendar, issued a statement Sunday opposing any such switch.
"FIS will submit a proposal to the other six international winter sports federations to sign a resolution against organizing the FIFA World Cup during the winter sports season in 2022," the Switzerland-based body said.
On Monday, winter sports officials gathered in Lausanne for a three-day gathering of all Olympic federations.
Bobsled federation president Ivo Ferriani said the FIS proposal had yet to be submitted to the AIOWF membership.
Fasel said informal discussions will be followed up at a next meeting at the Winter Olympics in Sochi, Russia, in February.
"I fully agree that we should have a discussion internally with the winter sports federations and have a common position," the Swiss official said.
Fasel said his own sport's national leagues would be affected by competing in November with football's World Cup, which draws the highest television ratings in international sports.
"We have the regular league games going on in the different countries so, for sure they will have less spectators because they will just watch the football," Fasel said. "Football is the No. 1 sport in the world this is like it is."