The possible role for Stephen A. Feinberg, a co-founder of Cerberus Capital Management, has met fierce resistance among intelligence officials already on edge because of the criticism the intelligence community has received from Mr. Trump during the campaign and since he became president. On Wednesday, Mr. Trump blamed leaks from the intelligence community for the departure of Michael T. Flynn, his national security adviser, whose resignation he requested.

There has been no announcement of Mr. Feinberg’s job, which would be based in the White House, but he recently told his company’s shareholders that he is in discussions to join the Trump administration. He is a member of Mr. Trump’s economic advisory council.

Mr. Feinberg, who has close ties to Stephen K. Bannon, Mr. Trump’s chief strategist, and Jared Kushner, the president’s son-in-law, declined to comment on his possible position. The White House, which is still working out the details of the intelligence review, also would not comment.