When approached for comment by the Herald this week, Goff would not go as far as calling on the Government to take action, saying only that he would support it if it did.
"Clamping is all too often a disproportionate and arbitrary response to a minor transgression," he said in a statement.
As mayor Goff did not have the power to make law changes to regulate parking enforcement on private land.
Currently, parking enforcement companies operating on private land are bound only by a voluntary code of conduct drawn up in December 2015.
"I would like to see those companies that are not part of this voluntary code change their view and become part of the code," Dean said.
An investigation by the Herald showed a staffer for Amalgamated Car Parking Services swooping on drivers' cars within minutes of them parking in a Mt Eden carpark.
Sitting in an unmarked car for hours on several evenings, motorists were made to pay $150 on-the-spot fees or risk being towed for twice the cost or more.
Until the Herald's investigation Dean said she had not looked into whether or not the code was working and wanted to get an idea of the scale of the problem before saying whether the Government would take action.
"Now the issue has been highlighted to me I will take an interest," she said.
"I will be taking advice on what is happening and we will take it from there. Certainly I am concerned that there is some unfair behaviour."
Dean planned to talk to her officials and have them deliver her a report on the issue, but would not give a timeline for when she expected that to happen by.
Labour's consumer affairs spokesman Michael Wood said the voluntary code regulating wheel clamping wasn't working, and he would be prepared to submit a private member's bill if the government didn't take further action.
There was no reason why work in the ministry shouldn't start by the end of the week, he said.
"We would call on the Government right now to sit down and have a really good look at what's going on."
