The clandestine manoeuvre last month came a day after the US renewed military strikes on Iran following a breakdown of negotiations between Washington and Tehran to end the war.
Trump had arrived in Turkey aboard a newer Boeing 747-8 donated by Qatar, but announced that he would leave on the old Air Force One "for old time's sake".
On 8 July, footage showed him boarding the presidential jet at Ankara airport.
But according to the Washington Post, he slipped off Air Force One on to a catering truck that had been elevated to plane level on the opposite side to where he had boarded.
He was then secretly taken to a smaller C-32A military aircraft - a modified Boeing 757 often used by the vice-president.
Defence Secretary Pete Hegseth boarded the C-32A separately using external stairs in an effort to make the flight appear normal, according to the newspaper.
Journalists and some White House staff boarded Air Force One and were reportedly told to close their window shades. They were unaware the president was no longer on board.
