American lawyer Michael Garcia is to meet officials from the Qatar bid in Oman, just 24 hours after fresh allegations were published about payments being made to African federations to win support for the campaign.
FIFA president Sepp Blatter is also facing calls to step down over the scandal - and Dyke refused to say whether the FA would back him for re-election, only that the world governing body needs to find conclusive answers to the allegations.
Garcia is investigating the bidding process for the 2018 and 2022 World Cups and is due to report later this year.
Dyke told BBC Radio Five Live: "FIFA has got to sort this out. FIFA has got to do their investigation and either it happened or it didn't happen.
"If it happened and there was corruption involved then clearly the process has to be re-run."
Asked about whether the FA would support Blatter, who is expected to announce next week that he is to stand again for election in 2015, Dyke added: "That's a decision that the FA will take at some stage.
"You have got to separate Sepp Blatter from this. Sepp Blatter as I understand it didn't vote for the World Cup in Qatar.
"I wouldn't give you that answer at the moment, the FA is going to make that decision."
The Sunday Times reported that it has 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.
In a statement, Qatar's bid committee said Bin Hammam had no association with them and that it was co-operating with Garcia's investigation.
The statement read: "The Qatar 2022 bid committee always upheld the highest standard of ethics and integrity in its successful bid to host the 2022 FIFA World Cup.
"In regard to the latest allegations from The Sunday Times, we say again that Mohamed Bin Hammam played no official or unofficial role in Qatar's 2022 bid committee. We vehemently deny all allegations of wrong-doing."
Issa Hayatou, the president of the African football confederation (CAF) and a FIFA vice-president, issued a lengthy statement on Monday denying a number of allegations made by The Sunday Times.
The statement called the allegations "fanciful" and "ridiculous", and added: "Mr Hayatou has never received any money from Mr Bin Hammam, the Emir of Qatar or any member of the Qatar 2022 bidding committee."
He said he was not aware of any payments being made by Bin Hammam to African federations, nor had he accepted any flights or privileges from Qatar 2022.
- Sports & Recreation
- Sepp Blatter
- Mohamed Bin Hammam
- Michael Garcia