Napier mayor Kirsten Wise supports the current policy and is keen to hear what the community thinks about extending it.
"Community voice is essential to the work we do and the decisions we make," Wise said.
"We want to help make our place as healthy and safe as it can be, so we need to hear what you think."
Hastings mayor Sandra Hazlehurst said she believes taking a strong position can improve public spaces.
"Hawke's Bay has a lot of beautiful public places that we all love using and putting in place policies that protect those spaces benefits everyone.
Feedback on the proposal can be provided to the councils until February 28.
The new policy, if agreed upon, would be put into place by the end of 2022.