European Commission President Jean-Claude Juncker indicated earlier this year after meetings with then prime minister Bill English that they hoped to have a deal within three years.
A deal with the UN traditionally takes five to 10 years to complete.
Ardern also has meetings with Canadian Prime Minister Justin Trudeau, Indian Prime Minister Narendra Modi, China's Premier Li Keqiang, Indonesian President Joko Widodo and the Philippines' President Rodrigo Duterte as well as attending the summit meeting itself.
Trade is also expected to be on the agenda with Mr Modi, with a focus on the Regional Economic Comprehensive Partnership which would give New Zealand greater market access into India.
"Also I'm going to continue to extend an invitation to Prime Minister Modi to visit New Zealand ... I think it would be fantastic to have a visit from him particularly for our Indian community in New Zealand," she said.
The summit overall is expected to focus heavily on regional security and preventing extremism in the region. The meeting with Mr Li is expected to cover the South China Sea but Ms Ardern does not anticipate raising the prospect of an extradition treaty with China.
"There are a number of other matters. We are for instance continuing to raise the use of the death penalty but actually at the moment most of the issues coming up are around regional security issues and North Korea," she said.
- NZN