"Was anyone above us who overtook us like 30 seconds ago?" A pilot hears the Albuquerque Air Route Traffic Control Center
The controller responds: "Negative."
Another pilot jokes that it's a UFO and the first pilot laughs and says, "Yeah."  The pilots of the first aircraft, a Learjet 36 from Phoenix Air, were still listening as the pilot asked a pilot to fly an Airbus A321 to look for American Airlines.
"We had a plane in front of you 37 [thousand feet] reported that something had passed over him and we had no [radar] goals, so let me know if you see something over them," says the controller.
One of the Learjet pilots continues, "I do not know what it was, it was not an airplane, but it was ̵
After about a minute, the American Airlines pilot says he saw something happened a few thousand feet above, but could not say what it was.
"American 1095, can you tell if it was in motio or just floating?" Asks the controller.
He replies, "Could not figure out if it was a balloon or whatever, but it was just really bright light or could have had a great reflection and was several thousand feet above us in the opposite direction."  If the American Airlines pilot theorizes it is a Google balloon, another pilot replies, "Dubious."
After a moment, another pilot interrupts the silence: "UFO."
The publication The recording comes months after the Pentagon has confirmed that a secret program exists to look into sightings of unknown flying objects. It was funded by the government from 2007 to 2012, ABC News reported.
The Phoenix Air pilot later said that he could not say what it was because the object was so bright, said Bob Tracey, Phoenix Air Group Vice President, ABC News
"He said the only thing be different, it's just that bright, "he said. "The glare was so intense that they could not understand it."
Despite the UFO jokes, Tracey said the pilot did not find the incident too disturbing.
"He said when he landed, he did not" I do not think about it for long, "said Tracey.
Listen to the full recording here.
ABC News contributed to this report .