An American Airlines pilot sounded pretty flummoxed by a "long, cylindrical object" zooming over his plane in New Mexico airspace -- ya know, not far from Roswell -- and now it's on FBI's plate.

The plane was traveling from Cincinnati to Phoenix Sunday afternoon when the flight crew spotted a strange, fast-moving object flying above them. The pilot called it in, first asking ... "Do you have any targets up here?"

He added ... "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 and went right over the top of us."

So, what the heck was it? If the FBI knows, it's not telling. FBI Spokesperson Frank Fisher tells TMZ ... the agency's "aware of the reported incident."

The reason the pilot asked about targets isn't necessarily a Roswell thing. They were flying near the Army's White Sands Missile Range ... however, the military's denied the object was one of theirs.

Fisher adds, "While our policy is to neither confirm nor deny investigations, the FBI works continuously with our federal, state, local, and tribal partners to share intelligence and protect the public."

Hmm ... the truth is out there. 🤔