"Let's not lose time on this. April-May is not an option because of the temperature," Valcke said on Wednesday in a statement provided to The Associated Press.
Valcke is leading FIFA's consultation to suggest which months to play after president Sepp Blatter rejected the traditional June-July World Cup period because of Qatar's searing desert heat.
Blatter has suggested a November start, though spring is supported by Karl-Heinz Rummenigge, chairman of the influential European Club Association.
Qatar hosted the Under-20 World Cup for FIFA in April 1995, and its 2022 organizing committee insists it can still fulfil a promise to host in midsummer in air-conditioned stadiums, training camps and public areas.
However, FIFA's own research into expected temperatures in Qatar seems set to rule out a World Cup in May, which would cause less disruption to the European season than stopping for most of November and December.
"The climate studies for April and May are quite similar" to June and July, Valcke said. "The best option is between mid-November and mid-January."
This year, temperatures recorded in Doha reached 41 degrees (105.8F) on May 11, while April daytime peaks ranged from 26 to 38 degrees (79 to 100F).
Though Qatar staged the 2011 Asian Cup from Jan. 7-29, Blatter has removed the January 2022 option as "totally disrespectful to the Olympic family" ahead of the Winter Olympics scheduled that February.
"We have also consulted our economic and media partners," Blatter said on Sunday in Doha, after meeting with the Emir of Qatar, who is a longstanding fellow member of the International Olympic Committee. "So many different partners are with FIFA and the Olympic Games so we cannot have the partners in two competitions at the same time."
Valcke is expected to outline a "road map" for FIFA's consultation process following a Dec. 4-5 meeting of its executive committee in Brazil.
European clubs and leagues are expected to be among the strongest voices in a process which is expected to run into 2015.