He said dealing with homelessness had traditionally been the role of central government.
"But I don't think we can sit back and say [it's] their responsibility.
"I think it's somebody that all of us need to contribute to. The Government, the councils around the country, our NGOs, our private sectors and each of us individually."
It was difficult to respond to it without knowing the scale and nature of the problem, he said.
Previous head counts of the homeless have mostly focused on the CBD and have been led by non-government groups.
The September survey would cover from Wellsford in the north to Waiuku in the south, and from Piha in the west to Hunua Ranges in the east.
Housing First Auckland project manager Fiona Hamilton said it would not be possible to cover every street within that area, which was about 5000sq km.
The survey would instead target places known for rough sleepers between 9.30pm and 12.30am. Volunteers would work in groups of three, and one of them would have experience with an NGO or social services.
It was designed to be non-intrusive and homeless people did not have to take part, though they would all be counted.
Once the data was gathered, the council would consider how it could respond.
While it has contributed some money to emergency shelters like James Liston Hostel in central Auckland, Goff said he wanted more lasting solutions.
The main mechanism for housing rough sleepers in the city was Housing First Auckland, an initiative which places homeless directly into houses before dealing with any mental health or addiction issues.
The council contributes around $500,000 a year to the initiative.
In the 13 months since it was established, Housing First Auckland has found homes for 420 people who had been living on the street, including 193 children.
It has achieved its goal of keeping at least 85 per cent of these in permanent homes after a year.
Hamilton said most of them had been housed by private landlords, who leased the houses to Housing First.
The most recent count of homeless in the central city, in 2016, found 177 people living on the street and another 51 in temporary accommodation.
A University of Otago study in 2015 estimated there were around 4200 rough sleepers across the country, and about 771 in Auckland.
Auckland Action Against Poverty coordinator Ricardo Menendez March applauded the council's plan for a head count but said it needed to be followed by a funding boost for public housing.
"It's difficult to imagine Government genuinely putting an end to homelessness with its current policies," he said.
"State homes are not being built fast enough and the current Housing First initiatives are only being made available to those considered to be chronically homeless."
