Mr. Trump has told others that he is concerned that a Biden Justice Department might seek retribution against the president by targeting the oldest three of his five children — Donald Trump Jr., Eric Trump and Ivanka Trump — as well as Ms. Trump’s husband, Jared Kushner, a White House senior adviser.

Donald Trump Jr. had been under investigation by Robert S. Mueller III, the special counsel, for contacts that the younger Mr. Trump had had with Russians offering damaging information on Hillary Clinton during the 2016 campaign, but he was never charged. Mr. Kushner provided false information to federal authorities about his contacts with foreigners for his security clearance, but was given one anyway by the president.

The nature of Mr. Trump’s concern about any potential criminal exposure of Eric Trump or Ivanka Trump is unclear, although an investigation by the Manhattan district attorney into the Trump Organization has expanded to include tax write-offs on millions of dollars in consulting fees by the company, some of which appear to have gone to Ms. Trump.

Presidential pardons, however, do not provide protection against state or local crimes.