Appearing before a parliamentary committee, Dyke said FIFA should publish in full a report into the bidding process for 2018 and 2022 being compiled by American lawyer Michael Garcia.
However, Dyke played down talking of stripping Russia of the 2018 tournament because of political tensions over Ukraine.
Garcia, who has been leading a FIFA ethics committee investigation into allegations of corruption surrounding the award of the 2022 World Cup to the Gulf state, will submit his report in September.
"If Mr Garcia shows that there have been corrupt activities, the whole thing should be reconsidered," Dyke said.
Dyke said he was convinced that the tournament would not be held in June or July if it was played in Qatar because of the intense heat, with a move to a cooler time of the year like November or December a certainty.
Dyke played down suggestions that Russia could be stripped of the World Cup as a punishment for the downing of a passenger plane over Ukraine last week which Western nations have blamed on separatists backed by Moscow.
"I think there will be a World Cup in Russia," Dyke told reporters after the hearing.
He had earlier told lawmakers that a decision to move a World Cup should not be based on "one week's events".
BLATTER TO STAY
Dyke said he believe that FIFA President Sepp Blatter would be re-elected if he stands again next year despite corruption allegations surrounding world football's governing body.
Blatter has been head of FIFA since 1998 and is expected to seek another term.
"If he runs again he will win," Dyke said, adding that European distaste for the methods of the 78-year-old Swiss was not shared in other parts of the world.
Dyke said that England, which lost out to Russia in the bidding for 2018, would focus on hosting European events for the time being.
He said Blatter's dislike for the British media, which has led campaigns to expose FIFA corruption, made it impossible to win a World Cup bid.
"Mr Blatter's view of the English media is such that he says why would you want to take it to England?" the former head of the BBC said.
The plain-speaking Dyke jokingly compared FIFA to a one-party state, in comments unlikely to endear him to Blatter.
Referring to a meeting of FIFA's congress in Sao Paulo he attended in June, Dyke said it was "like something out of North Korea at times - hail to the leader."
(Editing by Ed Osmond)
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