Mr. Scaramucci could not be reached for comment. His expected appointment was reported by the website Axios.

Mr. Scaramucci is close to Mr. Trump’s eldest son, Donald Trump Jr. He is also respected by Ms. Trump and her husband, Jared Kushner, who is a senior adviser to the president. And Mr. Scaramucci has a direct line to the president, whom he has known for years.

Even so, his appointment would be unusual, given his lack of a traditional communications portfolio. But he has been seen as an avid and effective defender of the president on television as the number of Mr. Trump’s open backers has dwindled.

Mr. Scaramucci was recently the subject of a retracted story by CNN that dealt with investigations into the Trump campaign’s ties to Russia. He accepted an apology from the network, but Mr. Trump’s supporters were gratified by Mr. Scaramucci’s approach to getting the story removed.

It is unclear if Mr. Scaramucci’s appointment will be blocked by Reince Priebus, the White House chief of staff. Officials have said Mr. Priebus helped jettison an earlier plan to put Mr. Scaramucci in the White House Office of Public Liaison.