However, the softly spoken Parker said it would be great to hold both titles.
"I want to get the titles in New Zealand before I look elsewhere overseas," he said.
"[Sonny Bill] is a great athlete and I have a lot of respect for him, so we will see what we can come up with."
Parker has sparred with Tatupu as an amateur and said he was looking forward to meeting the hard hitter in the ring on October 12 in Auckland.
Parker visited the Rotovegas Boxing Gym and Pak'n Save yesterday, signing autographs while talking to young fighters and fans from Rotorua.
The giant fighter has slimmed down since his last fight against Francois Botha, following a seven-week training regime in Las Vegas.
"It was intense, we trained six times a week, three times a day."
Parker said he was in great shape, after being tested in the 40C-plus heat for seven weeks.
His trainer Kevin Barry, who defeated Evander Holyfield in his early boxing career and trained David Tua, said Parker was one of the hardest workers he had come across.
"I have never worked with a young man who gives me 100 per cent every day, like Joseph does," he said. "He is a very tough fighter."
