Under Widodo, the Government has taken a hardline approach on the issue, confiscating and then blowing up 170 foreign fishing vessels with explosives over the last two years.
While this policy has proved popular with Indonesians, it has threatened to escalate tensions in the South China Sea.
New Zealand's Pacific Economic Development ambassador Shane Jones, who met with Indonesian officials in Jakarta this week, said the Indonesian Government was asking New Zealand for new solutions.
"They're very keen to draw on the New Zealand experience," he said.
"They want to know how, when you apprehend cases of egregious illegality, do you actually turn it into a legal win without blowing up the boat every time?"
The exact nature of New Zealand's support is still being worked out, but it is unlikely to entail Royal New Zealand Navy patrols in Indonesian waters.
"They're very well aware that our naval vessels are active in the Pacific," Jones said.
"But I did not receive a formal request in terms of our naval vessels."
Ministry for Primary Industries compliance operations manager Gary Orr said New Zealand had shown that it was capable of tackling illegal fishing in its own waters.
"Rather than blow a vessel up, we've actually been able to get some recompense for the transgression. That might be an option they want to consider.
"I know it's high profile to destroy vessels. But if there's an opportunity to recover some costs from the sale of the vessel, then maybe that's something they want to explore."
One of New Zealand's foreign policy priorities in the Pacific is protecting the US$4 billion tuna fishery, which is crucial to Pacific nations' economies.
Orr said that because tuna was a migratory species, New Zealand also had to keep a close eye on neighbouring waters.
"Tuna don't recognise boundaries. If you don't have good management practices in place in one part of that migratory cycle, then it impacts on the sustainability of the fish for everybody."
"You can't just have 80 per cent of participating countries managing it sustainably if the other 20 per cent don't. The stock will crash eventually."
The New Zealand Government is increasingly looking to develop its trade relationship with Indonesia to tap into its growing middle class and diversify its trade beyond China.
It already provides $90 million in aid to the country each year - more than any other country outside the Pacific.
