After she walked out onto the “Late Night” set, Meyers congratulated Conway on a well-run campaign and asked her whether Trump knew she was going to be on the show. “Do you think he’s watching?” Meyers wanted to know.

“I hope so. He’ll watch at some point,” Conway said, adding: “We’re fans.”

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Meyers, who has earned praise for his incisive political commentary — often aimed at the president-elect — smiled. “I don’t know if we are fans,” he deadpanned.

With the initial pleasantries out of the way, Meyers asked Conway whether she could “confirm or comment on the fact that the intelligence community has presented” the classified report to Donald Trump,” who had tweeted hours earlier in response to news reports: “FAKE NEWS — A TOTAL POLITICAL WITCH HUNT!”

“Well, guess what hasn’t happened, Seth,” Conway began. “Nobody has sourced it. They’re all unnamed, unspoken sources in the story, and it says it was based on a Russian investigator to begin with.”

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“I think it was based on an MI6 British investigator,” Meyers noted.

“Right, well one of those. And then it said that it also may have originated with a Russian investigator. It also says that Hillary Clinton and groups that wanted Hillary Clinton to win may have been behind the investigations themselves. And, most importantly, it says that the FBI is trying to confirm it. So nothing’s been confirmed.”

Conway continued: “And I have to say as an American citizen, regardless of your party or if you don’t like politics at all, which are many Americans, we should be concerned that intelligence officials leak to the press and won’t go and tell the president-elect or the president of the United States himself now, Mr. Obama, what the information is. They would rather go tell the press —

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“But the press report was about them going to the president,” Meyers said.

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“And it says that they never briefed him on it, that they appended two pages to the bottom of his intelligence report,” Conway said.

“I believe it said that they did brief him on it,” Meyers said

“Well, he has said that he is not aware of that,” Conway replied.

“That concerns me,” Meyers said.

“It’s not fair, and it’s not true,” Conway interjected.

“What’s not fair? That I’m concerned?” Meyers joked. “I assure you I am.”

“It’s not fair that people don’t give him his due,” Conway said. “He received an intelligence briefing. He made comments about it afterward. And I have to tell you there wasn’t very compelling information in terms of the nexus that people like to make between alleged hacking and the election results. Vladimir Putin didn’t tell Hillary Clinton to ignore Michigan and Wisconsin. She did that all by herself.”

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Meyers and Conway were able to find a common ground here. “I am not going to sit and argue with you that the Clinton campaign was a well-run campaign,” Meyers said.

“Or that the Russians interfered in the election successfully. That they interrupted our democracy,” Conway said.

“But shouldn’t we care if the Russians tried to interfere?” Meyers asked. “Whether it informed the election or not. I sometimes fear that the president-elect has no curiosity as to the amount they tried.”

“That is completely false,” Conway said. “He has enormous curiosity. I’m there every day with him. He has a number of different meetings every day — briefings and otherwise. He was curious enough to figure out America. He knew America when many other Republicans did not.”

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“That’s a pivot right there, Kellyanne,” Meyers said, before breaking into applause. “And by the way, no one does it better,” he added.

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In the interview, which ran more than 13 minutes, Meyers also asked Conway about the president-elect’s tweeting habits, his upcoming news conference and confirmation hearings for the president-elect’s Cabinet picks. Meyers also presented Conway with a wager of sorts.

“I’m going to make you a bet,” Meyers told Conway as they were wrapping up the interview. “I bet in the next four years we are not going to see the president-elect’s tax returns.”

“And I bet — and I know because this was talked about during the campaign — I bet that most Americans will really care what their tax returns are going to look like after he’s been president for four years,” Conway replied.

“I think that means you agree with me,” Meyers said.