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But one commentator and former world title holder believes the New Zealander's heavyweight champion days are 'long gone'.
Parker moved to 29-2 for his career following last weekend's split decision victory over Derek Chisora in Manchester.
Tony Bellew, a former WBC cruiserweight champion and now boxing pundit, said Parker is past his peak.
"He's not a bad fighter, but no," he told Sky Sports.
"I think his heavyweight champion days are long gone. I don't think he's the fighter that he was.
"Every dog has his day. Believe you me, I know that as well as anyone. I wish tomorrow I could come back myself, but I don't think he can reach those dizzy heights again now.
"I think he had his moment and as soon as the levels stepped up in competition, and the fitness level of the opponents that he's facing got better, it will show."
The Kiwi heavyweight conceded he took his "foot off the accelerator" against Chisora but blamed an elbow injury, sustained during the fight, for slowing him down.
It was the final fight in his deal with Matchroom Boxing and he is now eyeing an immediate re-match with Chisora, while Dillian Whyte and Andy Ruiz are the other possibilities.
"I must have taken the foot off the accelerator – the killer instinct sort of kicked in at the end. But I'll have to watch the fight to see what I did wrong," he told Newstalk ZB's Mike Hosking.
Parker conceded it was a very close call, and was unsure how it would go after the 12th and final round.
"It was very hard for us to tell, when the hand was raised I was very happy, very delighted that we got the win," he said.
"I wasn't quite sure…I felt I did enough mid rounds and picked him off with jabs at the end of the fight.
"It was a very close fight. A lot of people are questioning it but I believe I did enough to win.
"From the sound of it they want a rematch, and I'll take that in a heartbeat. A lot of people thought it went my way, a lot of people thought it went his way.
"The only way to solve this problem is to have a rematch and to see who the actual winner was.
"If we can make it on to the undercard of the Tyson Fury-Anthony Joshua fight it would be a great experience, and will be a great fight.
"I want to show exactly why I won the fight in the first place."
Parker will remain in England to train under Andy Lee, who replaced Kevin Barry after Parker's battling win over Junior Fa in Auckland this year.
"I know it will be a long term thing [with Lee]," Parker said.
"I showed glimpses of what I have worked on…it's early days, it's great to get away with the win, and keep progressing.
"I'll stay here to continue training, to work on the things I need to work on, and fight in July or August.
"Hopefully I'll show a lot more improvement in the next fight."
Parker said he would leave the match-making up to his manager David Higgins, as he positions himself for another shot at a world title.
"I don't care who I fight – I just want to be involved in the most exciting fight out there," he said.
"If it is Andy Ruiz I'll take it in a heartbeat…if it is Dillian Whyte I'll take it with both hands. We have to position ourselves for when the belt becomes available."