"I'm looking forward to a good relationship and a good friendship with Bill. I've invited him to come kayaking with me on Sydney Harbour and I reckon if he's fit enough to beat a champion shearer, he'd probably outpace me on the water.
"You go out really early in the morning, go out to South Head and watch the sun come up. That's pretty amazing, so we can do that together."
Despite the invite, English had no luck getting Turnbull to back down on Australia's controversial policy of deporting those who had served more than 12 months in prison.
Turnbull said he would not change his mind about the policy but insisted it was being applied more fairly now.
Key and English had both raised concerns about it, given some of those deported had lived in Australia since they were children.
Turnbull said he had followed through on his promise to ensure a smoother process for appeals and a number of deportation orders were being overturned on appeal.
"So it's working a lot better now than it was initially, at least from the point of view of New Zealanders, I believe."
Turnbull did not answer directly when asked twice if Australia had any concerns about sharing intelligence under the Five Eyes agreement with a Donald Trump Administration, given Trump's tendency to overshare on Twitter.
However, he said the agreement was valuable and would survive the Trump presidency.
Turnbull said the Five Eyes agreement between the US, Australia, New Zealand, Britain and Canada, was a cornerstone of transtasman security.
