There had been substantial private investment in car parking buildings, so it was important not to undermine that, he said.
City councillor Deon Swiggs asked staff to look into it.
"It's about getting people back to the central city to try it out. If they have a good experience, they will come back again."
Central City Business Association chairman Brendan Chase said the idea came up at a summit the association held and it would be good for business.
Another idea was if someone bought something at a shop or cafe, they could be reimbursed for their car parking fee, or could get a free ride home on public transport, he said.
More people were returning to the central city, and it was only going to improve, he said.