The aircraft appeared yellow and cross-shaped, and came near the executive jet around 5:54 p.m. on Sunday, according to wire reports.
Mr Trump was returning from a long weekend at his Bedminster, New Jersey, golf resort. He also visited his younger brother, Robert Trump, who passed away Saturday night in a New York hospital.
The drone did not strike Air Force One.
Federal safety officials have struggled investigating such events.
One reason is most commercial drones are small and weigh only a few pounds. Some military aircraft have been hit by them, but were not taken down or seriously damaged.
The remotely piloted aircraft are not supposed to fly higher than 400 feet.
As commercial drones became more and more affordable last decade, some aviation experts warned they would be hard for the government to regulate and prevent from causing havoc for large planes and helicopters.