The clip, released by the Kensington Palace Twitter account, features Obama asking Harry if he needs to speak faster or with a British accent during the interview.
Harry then jokes with his guest about avoiding long pauses during the segment unless he wants to see "the face."
"I don't want to see that face," Obama says after Harry gave a comedic, disapproving look.
Harry is interviewing Obama to discuss their shared interest in "building platforms for the next generation of young leaders," Kensington Palace said on Twitter. The interview will air on Dec. 26 on BBC News Radio 4.
Prince Harry's guest editorship of @BBCRadio4 Today programme on the 27th December will feature an interview with former US President @BarackObama. The interview focuses on their shared interest in building platforms for the next generation of young leaders. pic.twitter.com/HaBaW0F5pM— Kensington Palace (@KensingtonRoyal) December 17, 2017
"I'm nervous about this," Harry continues in the preview.
"It's fun. I'll interview you, if you want," Obama says.
Harry replies, "Let's keep it this way, I'd much prefer that."
Harry and his fiancee, U.S. actress Meghan Markle, recently announced that they will be tying the knot on May 19.