"I think that it is unlikely that this approach will lead to the kind of improvement that the city needs to see in our governance," she said.
She suggested asking Local Government New Zealand (LGNZ) to undertake or commission the review.
LGNZ president Stuart Crosby told the Herald he encouraged all councils to undertake governance reviews, so their arrangements continued to deliver for ratepayers.
"LGNZ stands ready to assist councils with these governance reviews, to ensure that their governance arrangements and practices provide direction and value for communities."
Earlier this week Local Government Minister Nanaia Mahuta said she wasn't considering commissioners for Wellington City Council "as yet".
"I certainly don't want to be the Minister for Local Government commissions and my preference is to ensure that local government and councils have the ability to undertake other avenues to be able to strengthen their governance or seek advice and support.
"They have their own professional entities that can offer that type of advice and I would urge them to look that way first."
Day noted the minister's encouragement of councils to make use of professional entities.
"LGNZ have the national picture and years of experience in local governance matters. I think they would ensure a robust and genuinely independent review", Day said.
"Working together on this is important if we all genuinely want this to improve the way we work – I am certainly committed to this. Everyone stood up yesterday when you asked them to. There is a lot of good will, lets make this work!"
Day, who is also chair of the Strategy and Policy Committee, said delegations made clear all councillors were responsible for reviewing governance.
"The reason for the delegation sitting with all councillors is because decisions about governance affect us all, given we are democratically elected by residents."
With that in mind, Day wanted more advice from officers about how the governance review could be made consistent.
Foster has been approached for comment.