"We'd like to see them off drugs, and the eventual aim is we'd like to see them back as productive members of society, that's the No 1 aim," he said.
The second aim was that "it's simply not a good look for a tourism city to have people sleeping in doorways, and I think it's an indictment on our society. What we're trying to do is shift people along into areas where they can get the help they need."
The notices could be issued for those sleeping or taking shelter in business sites outside of working hours, the council's Manager Community Strategies, Natasha Carswell, said.
They could be issued for private premises on behalf of the owner and in council parks, reserves and structures.
"Our street patrols will issue a warning, followed by a trespass order if appropriate, if they come across people sleeping in or leaving unattended gear in the specified areas."
If the trespass notice was ignored, police would become involved.
The council has recently begun foot patrols in the CBD, which were hoped to provide a presence, and reduce the antisocial behaviour associated with some rough sleepers who were also begging. These staff would be working with police.
Ms Carswell said they had received positive feedback about the patrols from retailers, with a reduction in complaints about anti-social behaviour occurring.
A few of those begging had been connected to the Outreach Service operated by social agency Whatever It Takes (Wit) for assistance.
The Government announced in July an investment of $325,000 over the next two years into Wit to help support the homeless in Napier.
The funding is set to provide the charity with the ability to support up to 20 individuals each year, including two homes that could house up to five chronically homeless individuals at a time while they are helped into more permanent accommodation.