"The FA board met yesterday and we want to know what was in it. What was the point of doing a full investigation if we don't know what was in it?" Dyke told Sky Sports News.
"We were one of the bidders for 2018. This was an investigation into 2018 and 2022. We want to know what it says, so we will certainly be pushing for it to be published.
"We are not alone - even Mr Garcia is pushing for it to be published."
The 2018 and 2022 World Cups were awarded to Russia and Qatar respectively, with controversy surrounding both bids since they were awarded.