He was still considering a run and his decision had to be "what the members want".
Tuiono said the members wanted the party to "push out in the most transformational way possible".
"The feeling I get particularly from young people, the people who are from the Green Left Network as well is they really, really want a strong independent voice that is not tethered to the Labour Party," Tuiono said.
"If that's not landing for them, then we need to do some reflection as a caucus as well," he said.
Tuiono defended members who had been "agitating" for change, saying it was their "right" to do so.
If he stands he will go up against James Shaw, who is so far the only person to confirm he will contest for his old job.
"We are pretty different people," Tuiono said of Shaw.
Shaw lost the role on Saturday after failing to get the 75 per cent support from delegates that he needed. Nominations for it are now open for seven days.
Other MPs, including Chloe Swarbrick and Elizabeth Kerekere have ruled out contesting it.
Today Shaw put up a post with a mea culpa and a promise to do better for members if he was re-selected.
In that post, Shaw admitted he had underestimated the concerns about him among the membership and had dismissed them as only those who did not want the Greens to be part of a government.
He said the vote had come as a shock to him.
"It's been clear for a while that there has been some disaffection with me, but I had understood that to be primarily among members who didn't support the party's decision to go into Government, or the compromises that come with the progress.
"I want to acknowledge that I understand that the vote wasn't just about that. If I'm honest, I've found it hard to get the mix right between being a minister and a co-leader and, quite clearly given the vote last weekend, I haven't quite nailed it."
He said he knew he needed to rebuild trust with some of the membership and was committed to doing that.
"As much as I have been frustrated by some of the criticism, as co-leader I need to listen and be there for anyone who has legitimate criticism. That is part of the job and that is why we have the mechanism to reopen nominations every year, to ensure that our co-leaders are responsive to those who do have concerns."
Co-leader Marama Davidson said while the co-leader contest was not "business as usual" it was still an "ordinary process" for the party.
"This is healthy, we are being called to reflect as a caucus whether we are being strong enough on climate on protecting our environment and on making sure that people have good lives, we are being called to account."
Davidson said Tuiono was "an incredibly skilled politician" but declined to endorse any candidate, saying that was up to members.
"He's been an activist and leader long before he became a member of parliament. And I really respect his work.
"I will not be endorsing any candidate, because that decision is up to the members."
Asked about Shaw's comments he had lost touch with members, Davidson said it was clear all of caucus had been asked to reflect on that.
Asked if she agreed with sentiments the Greens had pulled too close to Labour, Davidson said: "Not at all".
"I'm very proud when we are able to be quite politically different and push labour to go further and faster push Labour got to do more for planet and people.
"We have to keep reminding our members of that work, that we both have got stuff over the line, but we are also pushing Labour to be better."
On Tuiono saying he would look to revise the co-operation agreement with Labour, Davidson said again that would be up to members.
"That's a fair question and that again will be up to the members to assess."
