Sarah Huckabee Sanders, the White House press secretary, said she would not comment on a closed-door meeting where the joke was made.
The White House has not denied the reports, but Sadler reportedly called McCain's daughter, Meghan, to apologize.
The White House did not deny the comments in a statement obtained by PEOPLE, simply stating "We respect Senator McCain's Service to our nation and he and his family are in our prayers during this hard time".
But she ended her missive on a hopeful note: "That said I believe there are more good people than those who make the noise".
During the phone call, McCain told Sadler she needed to apologize publicly, and the White House aide said she would, according to the source. "I like people who weren't captured".
The nonprofit organization, Veterans of Foreign Wars, mistakenly emailed a draft release to reporters announcing the death of McCain, who has been at his Sedona ranch recovering from recent surgery and continues to battle an aggressive form of brain cancer.
Separately Thursday, retired Air Force Gen. Thomas McInerney said during an appearance on Fox Business Network that torture "worked on John" during McCain's five and a half years in captivity during the Vietnam War.
Messi breaks Clasico record in thrilling draw
With most of the players visibly exhausted and struggling to recover on defense, both sides had chances to get the win. Real Madrid had denied giving the La liga champions the guard of honour during the El Classico on Sunday.
"I don't understand what kind of environment you're working in when that would be acceptable and then you can come to work the next day and still have a job", she said on ABC's "The View". "Unfortunately, the testimony the American people heard from Haspel failed to address these concerns", said McCain.
After watching Haspel's Senate testimony Wednesday, McCain issued a statement saying that although Haspel is "a patriot" and a longtime public servant, her past work at the Central Intelligence Agency overseeing interrogation programs was "disturbing". And I want to say that since my dad has been diagnosed the past - it's nearly a year, July 19th - I really feel like I understand the meaning of life.
Haspel faced grilling Wednesday by the Senate Intelligence Committee about her role overseeing some CIA operations after the September 11 attacks.
"To say he's not a hero because he was a prisoner of war is stupid", Gerson added, alluding to President Trump's knock on McCain during the presidential campaign. Both cited unnamed individuals in the room when the disparaging remark was made by Kelly Sadler, a special assistant to the president.
The fallout dominated yesterday's White House press briefing and had some veterans and a U.S. Naval Academy graduate steaming.
Sadler did not immediately return a request for comment Sunday.
Her role in overseeing the use of torture by Americans is "disturbing", he says.