The air traffic controllers then contacted the American Airlines pilot to ask whether he had seen anything "pass over".
On 8 July, Roswell Army Air Field revealed they had found a "flying disc", which had crashed in the New Mexico desert.
The initial report came from N71PG, the Learjet, asking Albuquerque Center if traffic had passed above them.
The controller then asks the American Airlines pilot if he can keep an eye out for the object.
The Learjet pilot said he doesn't know what the flying object was, but he is certain that it wasn't a plane. "It wasn't an aeroplane but it was, the path was going in the opposite direction".
In newly released audio footage, the pilots and air traffic controllers can be heard discussing the baffling situation in almost unbelievable detail.
"Was anybody, uh, above us that passed us like 30 seconds ago?" the pilot said, according to a radio broadcast released this month by the Federal Aviation Administration. He said it was beaming light or had a big reflection.
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"UFO", someone responded matter-of-factly.
The location of the sightings was also about 500 miles west of one of the most famous UFO incidents in US history: The 1947 UFO "crash" at Roswell, New Mexico. Some believe it may have been one of the Google WiFi balloons, but the pilots are pretty sure that it wasn't.
He sees it too, saying: 'Yeah something just passed over us, like a, don't know what it was, but it was at least 2-3000 feet above us fast right over the top of us.
Based on the conversations, the UFO hovered above the eastern-bound airplanes in the opposite direction and was located a few thousand feet above the aircraft.
It's still not clear what the pilot saw, although another pilot would soon report the same thing.
"Other than the brief conversation between two aircraft, the controller was unable to verify that any other aircraft was in the area", the FAA's Lynn Lunsford told the New Times.
An FAA spokesperson said they frequently work with agencies in that area and "safely handle" aircraft of all types, including military, civilian and high-altitude weather balloons. The U.S. military said the debris was from a crashed weather balloon, but many speculated that the scraps were from a crashed alien flying saucer.