This is a reasonable question, one asked again in a recent post on The Cryptozoologist. After all, experimental aircraft have taken on a lot of odd shapes over the past 70 years or so, since the science of aerodynamics became less guesswork and more engineering in the years before World War II. You can find plenty of Internet claims and speculation about German disc-shaped aircraft, and all the other major powers had their experimental planes too, some of them very weird. But to stand in for "flying saucers" in the postwar world requires high performance as well as striking appearance, and I don't think it happened.
The reasons I discount disc-shaped aircraft, beyond the occasional experimental vehicle, is that the aerodynamics stink. They're hard to control. As with a flying wing, you are spreading the aerodynamic effects over this huge surface, much of it far away (relatively) from the ailerons and other control surfaces that give it direction. I don't believe for a moment the Nazis or anyone else developed a high-performance disc in the 1940s-1990s. That said, the sophisticated digital controls and other advances in the B-2 era might, I think, allow you to develop a high-performance disc today, but it would be a big investment for no real return unless getting the disc shape was the entire purpose of the project: payload would still be minimal. The exception would be if you got away from the jet propulsion system into some kind of propulsion that delivered thrust evenly around the disc (you can do that with jets, but the complexity and weight penalties will kill you, and the Coanda effect mentioned by some of the Nazi buffs is real but even less efficient.) "Revelations" by "insiders" about German or American disc aircraft never try to explain the engineering of the thing.
For those who are curious, I did try to come up with a practical disc in fiction: Send me an email if you'd like to read my story "The Old-Fashioned Way."