WASHINGTON — After days of reports that President-elect Donald J. Trump had requested a top-secret security clearance for his son-in-law, Jared Kushner, people close to Mr. Kushner said that was not the case. No such request has been made, they said on Wednesday, and he will not sit in on the president’s highly classified daily intelligence briefing.

But should Mr. Trump change his mind, former government officials and experts on classified information said he would have wide latitude as president to bring a family member into the most secret circles of the government.

“The president can authorize clearance for anyone he wants,” said Steven Aftergood, director of the project on government secrecy at the Federation of American Scientists. “It’s part of his commander-in-chief role. He has broad, essentially unlimited, access in this area.”

Like anyone else, Mr. Kushner would be subject to a background check by the F.B.I. But the president’s authority is so broad, Mr. Aftergood said, that he could override red flags — like fraud, huge personal debt or ties to foreign governments — that would disqualify other applicants.