Crowe, acknowledged as New Zealand's finest batsman, made his prediction as he revealed details of his battle with cancer.
He appeared to have beaten a form of lymphoma about two years ago, but said late last year the disease had returned.
Talking to journalists at Eden Park in Auckland, where once he dominated with the bat, Crowe said he wanted to be remembered as "genuine, real, authentic, not false, not masked".
"I'm picking a New Zealand v South Africa final. That's my gut feeling with South Africa due as well. We are going to win it one day and we're pretty good at home," Crowe said.
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Although doctors wanted Crowe to be in hospital, he said he now preferred to shun continued chemotherapy and wanted to stay home and try natural remedies.
Former All Black Grant Fox had given him supplements made from sea cucumber from Pacific Islands.
"The chemo is brutal and it was going to be a 100-day vigil so I thought it would be better if I just chilled at home and so far, so good," he said.
After several months of sleeping up to 14 hours a day he said he had been feeling good for the past three weeks and spent New Year with his cousin, the Oscar-winning actor Russell Crowe.
"He flew us up to his farm (in Australia) ... Had all the kids and cousins there," he said.
Crowe played in 77 Tests, averaged 45.36 and scored 16 centuries which still stands as a New Zealand record.