Appearing before a Culture Media and Sport Select Committee on Tuesday, Dyke explained that the allegations surrounding the bidding process for upcoming World Cups had forced them to reconsider their plans.
Instead, the FA want to focus on future UEFA competitions and England and Wembley Stadium are in the running to hosts matches during Euro 2020 as the tournament spreads itself across the continent.
"We've already taken the decision that we will not bid for FIFA tournaments – our decision is we will concentrate in the years ahead on bidding for UEFA tournaments," said Dyke.
"Would we leave FIFA? Not on our own, no. I don't think we should walk out of FIFA because within a week everyone has forgotten you. I don't think that sort of gesture-politics would help.
"I think trying to reform through UEFA and from the inside is the better way forward."
The FA has led calls for FIFA president Sepp Blatter to step down at the end of his fourth term in office, but the 78-year-old plans to run again for re-election.
Dyke does not believe that is the right move and thinks Blatter must go before any changes can happen at the highest level.
"We think there's a limited amount of time people should sit on the FIFA executive," Dyke added. "We voted in favour of that but most voted against it.
"It's that sort of reform that is needed to make sure we get proper turnover.
"Hopefully a new president coming in would take a look at the whole structure.
"A lot of the European FAs made it clear they didn't support Blatter but I'm afraid from the rest of the world he has overwhelming support. If he runs again he will win but I think it's unlikely we at the FA would vote for him."