"They realise many people will want to share in their happiness," the report said.
A spokesman for Prime Minister John Key's office, responsible for issuing royal invitations, said: "The Prime Minister has stated on numerous occasions he would welcome a visit to New Zealand by their Royal Highnesses, the Duke and Duchess of Cambridge.
"He has told them that we would love to have them here but he doesn't know when that would happen."
Government House spokesman Antony Paltridge said the agency was unaware of any plans for such a visit.
Prince George's first appearance to the world came in a storm of flashbulbs and cheering at just 27-hours of age.
Swaddled in a white shawl, he lay in the arms of his beaming mother; at her side, beaming just as proudly, his father. After a few moments on the front steps, the Duchess passed the tiny heir delicately to her husband, and the couple strolled towards the crowds.
The press fired questions. The din was constant. The royal parents seemed to be the only people remotely close to calm.
The Duke smiled.
"He's got a good pair of lungs on him, that's for sure," he said of his son. "He's a big boy, he's quite heavy. We're still working on a name so we'll have that as soon as we can."
Would it be George? The Duke laughed. "Wait and see, wait and see."
And we have. And it is.
"He's got her looks, fortunately," he said. "No no, I'm not sure about that," said his wife bashfully.
Nodding to his son's hair, the Duke added, "He's got way more than me, thank God."
The Duchess said, "It's very emotional, it's such a special time. I think any parent will know what this feeling feels like."
How about nappy-changing? "We've done that already," said the Duke breezily.
"He's done the first one," added the Duchess.
Then the Duke slipped baby George into a car seat, popped it into the back of their Range Rover and got behind the wheel to drive to Kensington Palace, where the Middletons were to hold a family celebration.