Blogger Steve Douglass recorded the transmission, which has been verified by American Airlines.
"We just had something go right over the top of us. I hate to say this but it looked like a long cylindrical object that almost looked like a cruise missile type of thing moving really fast. It went right over the top of us," the pilot told ground control.
According to a report by Fox News, the UFO could have come from White Sands Missile Range, based in New Mexico.
The sighting is the latest in a series of reported UFOs in the area over the years.
In 2014 and 2015, US Navy pilots spotted multiple UFOs traveling at hypersonic speeds in the area. The US military branded those sightings "unexplained aerial phenomena" and the mystery surrounding them remains.