'Qatar World Cup must be held in Nov/Dec'
The task force is to meet in Doha later on Tuesday for the third and final time.
Sheikh Salman bin Ebrahim Al-Khalifa, the Asian Football Confederation head, had ruled out May, the preferred option of Europe's top leagues and clubs, the BBC reported.
After the last task force meeting in November, Fifa secretary general Jerome Valcke said January/February 2022 or November/December 2022 were the preferred options.
But Sheikh Salman said a January/February World Cup was not desirable because it would clash with the Winter Olympics.
"We don't want it to collide during that period," the BBC quoted him as saying.
"Stakeholders are concerned about playing in the summer, so we have to change to winter. That's January or November. They have to make a choice, either A or B.
"But I think everybody agrees that in January or February it's difficult to play for the reasons that I mentioned before (Winter Olympics).
"The only option that I see is November/December."
The task force is to meet in Doha later on Tuesday for the third and final time and is expected to make a recommendation to the Fifa executive committee. On the basis of that recommendation, the final decision on the long-running saga should then be made in Zurich on 20 March.
The European Clubs' Association said on Monday they still hoped to push for a May World Cup at the Doha meeting to lessen the impact on their competitions.
Sheikh Salman hoped his proposal was "a done deal" even before the meeting, the BBC said. "Hopefully we can settle this issue once and for all," he said.