Dyke's comments come after The Sunday Times claimed it had gained access to millions of emails and documents which have highlighted payments made by disgraced former FIFA executive committee member Mohamed Bin Hammam.
The newspaper claims the documents show Bin Hammam made payments to football officials as part of a campaign to win support for Qatar's 2022 World Cup bid.
Sources with connections to Bin Hammam insist, however, he was not part of the Qatar bid team and was already building his power-base ahead of a challenge for the FIFA presidency.
The Qatar 2022 World Cup bid committee denied any wrong-doing in a statement on Sunday.
FIFA's chief investigator Michael Garcia is looking into the bidding process for the 2018 and 2022 World Cups and is due to meet officials from the Qatar bid in Oman next week.
Dyke said if corruption was proved then FIFA needed to act.
The FA chairman told Channel 4 News: "Some of this evidence on the face of it is quite compelling.
"If the evidence is there, that the process is corrupt, then obviously the process has to be looked at again."
In a separate interview with BBC Sport, Dyke added: "I think if it is shown it was a corrupt system and that the people who won used bribes and other influences to get the vote, then of course it has got to be done again."
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- Mohamed Bin Hammam