He said on air this morning "management and production argue she should come back on a periodic basis" but he felt Ardern "didn't want to be here" and "are we not better on this programme ... not having her on the show?"
"Give us the feedback," he said to listeners.
Hosking this morning spoke with Ardern about the transtasman travel bubble, and afterwards expressed frustrations about the interview.
Ardern last month scrapped her long-standing weekly appearance on Hosking's show.
At the time she said the decision was a month in the making.
Hosking accused her at the time of "running for the hills" and lacking backbone.
But the PM said no one could do every media slot - "people get news from a number of different sources".
Although the regular weekly slot was canned, Ardern said she, alongside her ministers, would continue to appear on the show "as and when issues arise".
After Tuesday's transtasman bubble announcement, producers of Hosking's show asked her to appear on the show and she agreed.
Throughout the interview the pair sniped at each other and, after the interview ended, Hosking erupted in laughter.
"We're involved in this discussion at the moment," he said.
"I don't want her back on the programme and your feedback appears to back that up.
"If she didn't want to appear on this programme that's fine, that's her issue, her prerogative, and she can own that but she doesn't come back.
"She doesn't get to pop up every now and again when the news comes out in the form of a bubble. Now to be fair to her, we did ask, and that's the productions side of this programme and she said she would so we're now in discussions - I don't want her back."
Hosking said producers and management had wanted Ardern to reappear on a "periodic basis" when there was "big news, big headlines".
"But then I look at what's just happened, did she answer the questions to your satisfaction, did we raise some reasonably salient points, did we demand some accountability and not get any, yet again?" he asked listeners.
"So the over-arching question I would ask, are we not better on this programme, you and I collectively, not having her on the show?
"She didn't want to be here, she doesn't add anything when she is here, so who's the winner and who's the loser, that I guess is up to you."
Hosking also earlier took a shot at other journalists after the PM announced last month she wouldn't be coming on his show regularly by accusing some of being "compliant" and asking her "softball" questions.
But today Newstalk ZB political editor Barry Soper fired back.
He said Hosking was arguing that he was the only one willing to ask tough questions to the PM and yet he was now walking away from that responsibility to keep her accountable.
"I'd say to Mike you can't have it both ways," Soper said.
"Accusing the media of not asking the right questions and being asleep at the wheel when you don't even plan to take the wheel yourself."
"You are going to turn down the opportunity to ask questions that you clearly consider are the right ones."
Hosking, meanwhile, declared that early feedback was firmly behind his belief the PM shouldn't come on his show based on a selection of texts he read out on air.
"Our prime minister lives in a fantasy world," said one listener.
"Oh my god, how can you stand it? How patronising is this woman," wrote another.
"Why do you waste your time?
"My God Mike how long did she have to prepare for the interview? Six weeks and nothing's changed. And so it goes and goes," read the host.
An NZME spokesman said the company had no comment. NZME also owns the NZ Herald.
