Football Association chairman Greg Dyke believes that Sepp Blatter will be arrested and forced out of Fifa within a "couple of months".
The 68-year-old also said England would not stage the 2018 or the 2022 World Cups, in case they were taken away from Russia and Qatar should corruption claims linked to the awarding of either tournament be proven, the Independent reported.
Blatter is said to have known about a 10 million dollars payment, which was sent to former vice-president Jack Warner from a Fifa bank account.
Ahead of the G7 meeting in Germany Prime Minister David Cameron said current events had revealed a "stark truth" about Fifa, and there was a need for the body governing football to be cleaned of corruption.
Blatter's resignation presents an opportunity to do that, he added.