Harold Mayne-Nicholls, who is considering challenging Sepp Blatter for the Fifa presidency, said the event could still be staged in the summer, But the ex-Chilean football chief said some games would have to start as late as 1am to avoid the worst of the heat.
"You could play the first games at 9pm, the second games at 11pm and the third matches at 3am," he told BBC Sport.
It is expected that the Qatar World Cup will be moved to winter in 2022 to avoid searing temperatures, with a November/December tournament currently being looked at by world football's governing body.
But Mayne-Nicholls said such a solution would be "chaotic" to most major leagues around the world.
Qatar was controversially awarded the 2022 World Cup by Fifa's executive committee in 2010.
Mayne-Nicholls had expressed serious concerns about conditions in the Gulf state, when he led Fifa's technical commission which assessed each bid for the 2018 and 2022 tournaments.
Now he has come up with a novel solution to one of the biggest dilemmas the sport has ever faced.
"You'd change everything. It would be a couple of hours behind in Europe, and that would help TV," he added.
Blatter has suggested a switch to November/December 2022 is almost inevitable, although another possibility is to stage the tournament in January and February.
But Mayne-Nicholls said that would also mean a clash with European football leagues, as well as the Winter Olympics and Super Bowl in the United States, and that a slightly earlier summer tournament should be considered.
"You could move it towards May, until the middle of June", he said.
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