The idea that a couple of teams could be intentionally drawn together - or kept apart - by heating or cooling the balls in the pot has long been the stuff of fans' conspiracy theories.
And Blatter, who was thrown out of FIFA and banned from football for corruption, told one of Argentina's biggest and most-respected newspapers that he had personally witnessed a draw being fixed.
Blatter made his comment as he was quizzed about the easy group that Argentina was drawn in during the last World Cup - and insisted while all the World Cup draws he'd been involved with were "clean to the last detail", he knew of other draws which had been fixed.
"Of course, you can put a signal in the balls, warming them or cooling them," he told La Nacion.
Rather shocked, the interviewer pushed him for detail: "Cold balls and hot balls. That exists then?"
The random draws in football are allegedly not so random as you thought, according to Sepp Blatter
Image credit: PA Photos
Blatter then confirmed that he had seen the practice in action:
"It didn't exist at FIFA, but I was a witness at draws, at a European level, where that happened. But never at FIFA. It certainly can be done, but in my time it never happened. Never."
La Nacion's reporter Sebastian Fest then pushed for more detail on how exactly it was done.
"They put the balls in the freezer beforehand. It's a simple thing to compare the balls and determine which are cold and which are warm. The moment you touch them you know."
It's hard to know how to see this one. On the one hand, there could be no witness less credible than Sepp Blatter, no man with more of an interest in pointing out that he was far from the only man involved in footballing skulduggery over the past few decades.
On the other hand, it's undeniably fascinating to hear this "confirmation" - such as it is - from the most well-placed of sources of a practice which has assumed almost cult status in the mythology of footballing conspiracy theories.
We may never know for certain if the claims are true or not. But given what we know of the things that are true about what has happened in football's corridors of power, this would be one of the mildest and least-harmful of the many alleged offences.