The former US president is one of the guests in the talk show host’s new six-part Netflix series “My Next Guest Needs No Introduction with David Letterman”.
Mr Obama recalled the time he and his youngest daughter Sasha danced with Prince, a few months before the singer’s death in 2016.
He told Mr Letterman: “This was probably three or four months before he died, and Prince asked Sasha to come up and dance, and she is an excellent dancer.
“Sasha pulls me up, which surprises me because she always mocks my dancing, I have dad moves.
“And I think the key is what we call ‘staying in the pocket’, you’ve got to stay in the pocket, because I think everybody here knows dads who get out of the pocket, and they’re trying stuff that they really can’t pull off and they start, like, doing karate kicks and all kinds of stuff.”
Mr Letterman’s new series also sees him interviewing high-profile guests including Hollywood star George Clooney, activist Malala Yousafzai and rapper and music mogul Jay-Z in front of a studio audience.
Following the launch of the series on the streaming service on Friday, January 12, a new episode of the talk show will then be made available every month.
Each hour-long episode will see Mr Letterman conduct wide-ranging interviews with his subjects while also digging deeper on a specific topic relating to the guest in question.
It marks the first talk show the broadcaster has hosted since he stepped down from his long-running Late Show with David Letterman in 2015.
Additional reporting by Press Association