Barnett said the Auckland business sector would be "comfortable" with the ports company being listed again on the NZX, or leased out, or a part sale to the Government.
But the chamber believed the Government stepping in wasn't the best option.
"It doesn't actually fix the problem. It would be a very temporary fix. Probably local government as a whole at this time needs to look at the billions of dollars of assets they sit on and ask whether they are assets they should be sitting on."
It was an issue Local Government NZ could think about, he said.
Because Auckland port was "not an asset you can buy and pick up and take away", the council would need to have a regulatory role, even under another form of ownership.
The future of the Ports of Auckland has been the subject of recent debate. Various external reports have concluded the operation's time in CBD is limited, for economic and environmental reasons. Advocated alternative operational sites include a shift to Northland's Northport and new-build ports at Manukau Harbour or the Firth of Thames.
The chamber, which Barnett said had kept a low profile during the location debate, recently proposed a port for NZ Inc for the next 100 years-plus be developed on an island in the Firth of Thames.
That proposal did not envisage either local authority or Government ownership of the asset, Barnett said.
On Barnett's call, Mayor Phil Goff repeated his long opposition to the sale of strategic assets "especially ... at a time when values would be at historic lows due to the pandemic and global recession".
"The port company already operates commercially, and provides commercial returns to the council through dividends, reducing the council's reliance on rates revenue and lessening the burden on ratepayers," Goff said.
"Council is undertaking non-strategic asset sales as part of its response to the financial impact of Covid-19. The Emergency Budget passed in July provides for the sale of $224 million worth of non-strategic assets and surplus properties.
"While the future location of the port is still to be decided, I do not believe it makes sense to talk about putting it on the market, because it would be unsaleable until that matter has been resolved.
"I believe strongly that the ownership of the port land should remain in public hands because the development of that land is critical to the future shape of the city.
"I have also been clear publicly that I am in favour of a progressive shift of the port to a new location, to free up prime land for more valuable uses and to provide greater public access to the waterfront.
"The sale of the port to private interests would significantly undermine the ability to proceed with relocation once a suitable site has been identified," Goff said.
Darby's proposal for the Government to take a 50 per cent stake in Auckland's port has been formally sent to Cabinet ministers, including Finance Minister Grant Robertson.