Blatter announced this week that he will step down despite winning a fifth term as president, following a string of arrests as part of a US Department of Justice probe into corruption within the world governing body.
The 79-year-old Swiss has pledged to instigate reform of the organisation before standing aside following a new election sometime between December and March 2016.
But Dyke, 68, told The Guardian website: "He'll be gone.
"He won't last. He can't last more than a couple of months. The one thing you discover if you run an organisation is that the moment you say you're going, you've gone. He's dead. It's over. If you resign, you resign."
Asked if he would put money on Blatter being arrested, Dyke replied: "Yes."
Dyke also dismissed suggestions that England could step in to host the World Cup in 2018 or 2022, after Swiss and US authorities launched probes into the bidding process, in which Russia and Qatar, respectively, prevailed.
England made an unsuccessful bid to host the 2018 tournament and Britain's Culture, Media and Sport minister, John Whittingdale said on Thursday that it was therefore in a position to host the 2022 event.
Dyke also criticised the London mayor, Boris Johnson, for saying England could step in "because it looks like we're doing it all for our own personal gain".
He added: "We won't have the World Cup in 2018, and we certainly won't have it in 2022."
Blatter has previously accused the British media of "racism" for raising doubts about the much-criticised joint-bidding process for the 2018 and 2022 World Cups, much to Dyke's displeasure.
"Blatter hates the English. He hates the FA," the former television executive added. "And he hates the British media. Blames them for everything."
Meanwhile, in rejecting claims the FA is unpopular in certain parts of the world, Dyke declared that "there are a set of values which you find in western Europe, and in America, and in Australia, that don't apply everywhere".
Elaborating, he said: "My experience in Africa is that when people go into politics in Africa, it's incumbent upon you as part of that to look after your family. That's just cultural, it's a cultural difference."
