Ardern responds with a laugh, saying "he has a real voice for radio, doesn't he".
They then played another question about the vaccine before saying "your thoughts Jacinda?".
"Do you actually want an answer," she said, but was told by the duo, "no we don't need the answers."
Ardern said: "Okay, because I was perfectly willing to give them."
It was the second time Hosking was mentioned during the Prime Minister's media round this morning.
At the end of Ardern's appearance on ZM, host Vaughan said: "We hope Mike Hosking heard it ... and we hope that's how you retain your regular chat with people."
"You are very unfair on your journalistic integrity there Vaughan," Ardern said in response.
Meanwhile the Prime Minister also shared she and partner Clarke Gayford will be setting a date for their wedding this Easter.
It comes nearly two years on from when the couple got engaged over Easter at Mahia during a break at Gayford's family bach.
Adern told ZM presenters, Fletch, Vaughan and Megan, she would not be getting married this Easter as "we are not ready yet".
But she said she and Clarke have would finally be sitting down to start planning their wedding.
When asked what part of the wedding she would be planning, she laughed saying: "Telling people a date, just the basics really."
Vaughan responded saying: "I thought you were going to ask me for advice but my wedding was 20 years ago and I didn't really have much to do with the planning."
Gayford proposed to Ardern at the top of a hill with a diplomatic protection squad officer nearby.
News of the engagement only emerged because a reporter attending the Pike River ceremony saw the Art Deco style ring on Ardern's left hand and asked Ardern's office about it.
The office later confirmed the news.
Ardern also told the ZM's crew she would likely get the vaccine before the general rollout.
"I'm waiting. I don't want to be a queue jumper… but I also take very seriously public messaging about it being safe."