Obama then says jokingly: "So you actually, er, you actually talk to the New Zealanders?"
Turnbull takes the question seriously and answers: "I do, look, he is a real role-model."
Obama, changing tack: "Nah, he's a wonderful guy. And he and I have become good friends. And not just because we play golf together."
A video of the conversation was posted on the Facebook page of Australian state broadcaster ABC News.
Alongside the video, ABC News wrote: "Microphones have once again captured an exchange between Prime Minister Malcolm Turnbull and US president Barack Obama on the sidelines of APEC."
It then added: "The pair were caught comparing notes on their favourite world leader."