The threat emerged on the final day of Trump's visit to Ankara for the NATO summit amid heightened tensions with Iran, the source said.
The Secret Service deemed the threat to be credible and imminent, prompting an extraordinary operation to conceal the US president's movements. The source on Wednesday declined to say where the intelligence came from but said officials had little time to prepare and devised the plan at the last minute.
Trump and a small group of aides used a catering truck to surreptitiously switch them from the big blue-and-white presidential aircraft to a smaller, nondescript C-32A jet for the flight out of Turkey on July 8, while Air Force One departed separately carrying senior administration officials, White House staff and the travelling press corps, according to the source.
Trump told reporters on Tuesday he made the switch at the direction of the Secret Service, which is charged with presidential security. He flew from Ankara to a refuelling stop in Britain without incident.
"I think actually the plane that I flew on was at greater risk," he told reporters, without providing evidence.
"... it was at greater risk because that would be the plane I think that they would be more likely to go for."
The threat may have been a new type of heat-seeking missile that homes in on hot aircraft engines and has become an increasing concern for military planners, said Douglas Birkey, executive director of the Mitchell Institute for Aerospace Studies.
They are harder to detect than traditional radar-guided threats and "can kind of come out of nowhere" because they don't send out detectable radio waves.
US presidents, including Trump, have occasionally travelled under secrecy when visiting war zones or high-risk regions in order to maintain security. But those trips typically involved advance notice for journalists travelling with the president.
The source said the Secret Service did not have the luxury of time in Turkey.
"They were scrambling to head off what they thought was a credible, imminent threat," the source said.
The Washington Post first reported details of the operation this week, more than a month after it was carried out.
The New York Times reported US officials were alarmed to discover that Iranians knew where Trump was staying in Ankara, including the exact floor of his hotel.
On board the Air Force One jet now seen as a decoy were Secretary of State Marco Rubio, who the source said was briefed on the manoeuvre; Treasury Secretary Scott Bessent; White House communications director Steven Cheung; and a number of other aides plus the typical 13-person press pool.
White House deputy chief of staff Dan Scavino, executive assistant Natalie Harp and director of Oval Office operations Walt Nauta made the move in the catering truck with Trump, the source said.
Some media commentators and lawmakers have questioned whether the operation left Trump's aides and journalists travelling with him at risk aboard the plane presumed to be carrying the president.
The source said it was determined that it was in Trump's best interests to keep the ruse secret as hostilities escalated with Iran, which borders Turkey.
Turkish officials did not immediately comment on the purported threat.