Michèle Flournoy Alex Wong/Getty Images When Michèle Flournoy met with President Donald Trump's aides at Trump Tower about the possibility of taking a top Pentagon position, one of the first questions she said she was asked was, "What would it take for you to resign?"

Flournoy, who was an undersecretary of defense under President Barack Obama and widely considered a top pick for defense secretary in a Hillary Clinton administration, told The New Yorker that considering whether to join the Trump administration made her feel physically unwell.

"I lost a lot of sleep and felt sick to my stomach," she said.

The founder of the think tank Center for a New American Security, Flournoy was torn about the decision, in part because of her admiration for Defense Secretary James Mattis, for whom she would have worked directly.

Flournoy told The New Yorker that Mattis "has more integrity in his little finger than almost anyone in Washington," but that she was disturbed by Trump's vetting process, which was conducted in part by a group of aides with no national security experience. And she was apparently alarmed by Trump's aides asking what it would take for her to resign, according to The New Yorker.

Ultimately, she told Mattis she couldn't take the position.

Only two of the top 57 civilian posts in the Pentagon are currently filled, in part because dozens of the most prominent mainstream Republican national security and defense experts signed letters during the campaign announcing their view that Trump is unfit for office. The president is opposed to bringing on anyone who criticized his candidacy, according to The New Yorker.

The White House did not respond to a request for comment.