The source added that the draft, the contents of which were reported by The New York Times, is in fact an administration document being circulated to various agencies.
But the White House said Wednesday that the circulated paper was not an official administration product.
"It is not a White House document. I have no idea where it came from, but it is not a White House document," White House press secretary Sean Spicer told reporters.
The publication of the draft, along with Trump's interview with ABC in which he said that "torture works," has raised concerns that his administration might seek to revive certain interrogation techniques like waterboarding. Trump did add that he would defer to his Cabinet as to whether he would adopt such policies.
Sen. Mark Warner, the top Democrat on the Senate Intelligence Committee, addressed these concerns during a Democratic lawmaker retreat in West Virginia, telling his colleagues he had spoken to Pompeo and that the CIA chief was just as surprised as the senators to learn of the document in question.
Warner added that Pompeo told him that he had not been informed of the memo in advance and wasn't aware that it was a White House document.
During his confirmation hearings, Pompeo said he believed torture to be illegal and that he would not order waterboarding or other enhanced interrogation practices.
But in a series of written responses to senators' questions, Pompeo did leave the door open for reviving some of the techniques, should experts say their prohibition harmed intelligence gathering -- but only if the current laws prohibiting them were changed.
"I think the director of the CIA has made it clear he's going to follow the law," Senate Majority Leader Mitch McConnell told reporters at the Republican retreat in Philadelphia.
"Torture is not legal and we agree with it not being legal," Speaker of the House Paul Ryan added while appearing alongside McConnell.