President Trump on Monday is expected to appoint Joseph Nocella Jr., a Long Island district judge, to be the interim U.S. attorney for the Eastern District of New York, according to four people with knowledge of the matter.

If he does so, Mr. Trump would sidestep the objections of Senator Chuck Schumer, the New York Democrat and minority leader, who had said he would block Mr. Nocella’s nomination along with that of Jay Clayton, Mr. Trump’s pick to lead the Southern District of New York. Mr. Trump named Mr. Clayton the interim U.S. attorney, and he is expected to do the same for Mr. Nocella.

Mr. Nocella, who arrived at the U.S. attorney’s office Monday morning, was to be sworn in by the district’s chief judge in a private ceremony in the afternoon, two of the people said.