This week's revelations surrounding doping in Russian athletics has implicated the country's sports minister Vitaly Mutko.
Mutko, who is a FIFA executive committee member, headed Russia's successful 2018 World Cup bid.
Speaking at the Birmingham County FA yesterday, Dyke said: "I have not seen any evidence of corruption in the application for Russia's World Cup bid.
"There's a lot of journalism being done, very good journalism I think, on whether or not the Qatar World Cup bid was tainted but I haven't seen it for Russia. But you do wonder having seen the events of yesterday."
Sepp Blatter, FIFA's suspended president, suggested the decision to award the World Cup to Russia was a foregone conclusion, rendering England's £21 million bid a waste of time.
"Mr Blatter's comment implies it was all fixed for Russia long before we were all bidding, in which case why were we all bothering?" said Dyke. "I haven't seen anything yet that implies Russia did anything wrong in this bid.
"This is about Mr Blatter and some other people on the executive of FIFA deciding that in advance who should win before they'd seen all the bids."
When asked whether England could host the 2018 World Cup, Dyke said: "I don't think we've thought about it.
"What we're interested in is getting a reformed organisation."
German FA president Wolfgang Niersbach resigned this week over a controversial €6.7 million payment to Fifa that was allegedly used to bribe officials to vote for the country to host the 2006 World Cup.
"It is like a soap opera," said Dyke. "Every week something is happening, you begin to be convinced that almost no World Cups have been allocated without a pile of bungs don't you."