In an article accompanying the interview that was taped on Saturday, Mr. Stephanopoulos suggested that Mr. Cohen, who once claimed that he would “take a bullet” for Mr. Trump, had “strongly signaled his willingness” to work with federal prosecutors — even if it put the president in jeopardy. Echoing that sentiment, some legal experts said that Mr. Cohen’s assertions were the clearest sign yet that he had changed course and could be on the verge of cooperating with the government.

“I viewed his statements as saying, ‘I’m going to cooperate if I can get a good deal,’” said John S. Martin Jr., a New York lawyer who has worked as both a federal judge and a federal prosecutor. “When he talked about loyalty to his family, what he seemed to be saying was he wants to limit his exposure and potential jail time. That’s cooperation.”

But while acknowledging that Mr. Cohen certainly sounded like a man in search of a cooperation deal, other legal experts said that prosecutors almost always prefer to negotiate such deals in private — not on morning television shows. The United States attorney’s office in Manhattan, which is investigating Mr. Cohen, and the office of the special counsel, Robert S. Mueller III, which is looking into ties between the Trump campaign and Russia, have both been all but silent about their work so far. It would be highly unusual, the experts said, if Mr. Cohen had gone on ABC to make his case for a cooperation deal in front of millions of TV viewers.

“If he really wanted to send a signal that he was looking to cooperate, he could just pick up the phone and call the prosecutors,” said Matthew Miller, who served as director of public affairs for the Justice Department under President Barack Obama. “He wouldn’t have to do this complicated dance in the media.”

Mr. Miller offered a different theory on Twitter on Monday: Mr. Cohen’s interview was likely directed at the president as a “not-so subtle request for a pardon.”