Mr Henare has put up his hand for the role currently held by Lockwood Smith, who will leave to become High Commissioner in London later this year.
Mr Henare said he raised it with John Key but would not say what the Prime Minister's response was.
"At the end of the day some people thought he wasn't going to be a good Prime Minister and he's turned out to be a wonderful Prime Minister."
Mr Henare refuted that he hadn't shown much "niceness" while in the house, adding to the "argy bargy" of Parliament.
"I've played the game in the house; so I know how to be bad, I also know how to be good."
"All I'm saying is that I'm putting my hand up and I want an opportunity."
Labour MP Trevor Mallard said Mr Henare would make an interesting Speaker of the House and joked he could be his deputy.
Mr Mallard and Mr Henare are known for their tumultuous exchanges in the house, as well as a punch-up between the pair in 2007 after after the National MP accused Mr Mallard of being a hypocrite.
"Clearly he's a very experienced member, he's got some ambition and he should be congratulated for that," Mr Mallard said.
"I think Tau can be a wonderful gentleman on occasions. He is a very interesting character and I look forward to his case."
National MP David Carter was also in the running to be New Zealand's next Speaker of the House.
He said it was a decision that would be led by the Prime Minister.
"I am enjoying my job at the moment and I think I am doing a good job as Minister for Primary Industries and Local Government, I'm continuing to do the best job I can.
The Speaker is elected by a vote of Parliament and candidates nominate themselves, although in practice it is usual for a government to decide who it will be, with some consultation with the Opposition.
- Kate Shuttleworth of APNZ
