Ken Kurson, a friend of President Trump’s son-in-law and adviser Jared Kushner, and a former editor of The New York Observer, the newspaper owned by Mr. Kushner’s family, confirmed on Friday that he is under consideration for an unpaid position with the Trump administration.

As part of a background check, the F.B.I. recently visited The Observer’s offices and has conducted interviews with journalists who have worked with Mr. Kurson, according to two people familiar with the matter. Such checks are standard for anyone who is up for a post in a presidential administration.

In an interview, Mr. Kurson described his possible appointment as an “honorary type position.” He added that it would be “like one of those boards, where there are several members.”

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

Before he joined The Observer in 2013, Mr. Kurson was a speechwriter for Rudolph W. Giuliani. He was also the co-author of Mr. Giuliani’s 2002 book, “Leadership.” Last May, he left The Observer for a job as a senior managing director at Teneo, an international consulting firm whose founders include two longtime advisers to former President Bill Clinton.