He might as well have been calling into “Fox and Friends,” or giving one of his cabinet meeting monologues. For two men with such a twisted history, it was an oddly impersonal and empty exchange.

This was not for Mr. Cohen’s lack of trying.

“You may remember, you may remember, that following morning,” he said at one point, “you called me into the office after, and then you gave me one of those traditional Trump slaps on the shoulder, and you said to me, ‘F— them, you’re stronger than them, we’ve got this …’”

Mr. Trump said that “we’re doing really well in the polls” and that “the economy has never been stronger.”

“Boss,” Mr. Cohen said, teeing up another “remember when” moment. “I literally used to analyze the polls, right? And you remember how much attention that I used to pay to that methodology? I would come in, I would say to you, ‘Oh, you know, they’re claiming that you’re 31 percent, that you’re underwater.’ But I showed you that …”

“The polls are crooked,” Mr. Trump replied.

“Exactly,” Mr. Cohen said.

Mr. Cohen had been hyping up the interview on the radio and on cable news and on social media as an epic homecoming. Shortly before he played his conversation with the president, Mr. Cohen told another host on his radio station: “This is the Donald Trump that I remember. This is the one that acts, and is acting, like the friend that I remember him to be.”