Trans-Pacific Partnership Agreement (TPPA) countries are "inching closer" to sealing the deal, with Prime Minister John Key hoping some hobnobbing at the United Nations could make some progress.
Mr Key is heading to New York next week to meet with world leaders for the 70th UN General Assembly, where US President Barack Obama will be hosting a leaders' summit on countering Islamic State and extremism.
It is the first time Mr Key will be at the UN since New Zealand was voted onto the Security Council.
He says trying to push the TPPA will be among his top priorities.
Since a round of trade talks ended without a deal in Hawaii recently, Mr Key says there has been "quite a lot of discussion going on behind the scenes".
"I'm not quite so confident as to say I think a deal will be concluded at the UN or in the next week or two, but I think quite a lot of progress could be made. We are inching closer," he said at his post-Cabinet news conference yesterday.
Mr Key says he will see Mr Obama at his leaders' summit and also possibly at a cocktail party on Monday.
Asked what his top priority was if he managed to get a one-on-one chat with Mr Obama, Mr Key said: "TPP, bluntly".
"The message is I think we should get a deal done, I think it's in New Zealand and the United States' interests to complete the TPP."
While there had been progress on a number of areas, Mr Key believes more work needs to be done for the dairy sector.
"I think we're a long way away from saying we're in the best place we can be for dairy so I wouldn't want to give that impression because I don't think we are.
"In the end, we'll settle on hopefully the right place for dairy."
During his week at the UN, Mr Key will deliver a speech in the general debate on October 1 and will also hold a number of formal and informal meetings at the UN as well as the New York business community.
Around 160 world leaders are expected to be at the UN during the week, in which the the Sustainable Development Goals are set to be adopted.