He said the Gulf states fell into the same category.
"Helen Clark identified in the early 2000s that it is an area in which we could do more business, and I think given the size of countries like Brazil and Mexico and Colombia, over time there is a lot of business for New Zealand there."
The Government produced its Latin America Strategy in 2010 aimed at strengthening ties with the region - but a Trade and Enterprise report on progress a year later observed that there was a need for a greater focus on building political links, especially at a head of state level and with a particular focus on Brazil.
There are hopes that the Prime Minister's visit will be a "game changer", particularly in Brazil - considered the least outward-looking of the four nations in question. It is the region New Zealand has to work hardest in as it does the ground work on a trade agreement with the Mercosur Latin American nations not involved in the TPP, led by Brazil.
Other issues that will take up most of Mr Key's time include:
Colombia
While New Zealand's ties with Chile and Mexico go back decades, links with Colombia are more recent. Mr Key will be the first New Zealand leader to visit Colombia, where he will meet President Juan Manuel Santos.
"Colombia is quite a big country and it's growing very rapidly, It's had very solid growth year-on-year. So it's likely to emerge as quite a significant player over time in Latin America. That's one of the reasons we are going there. They are quite like-minded on matters like trade and the like. So we are hopeful we can make [progress]."
Trans Pacific Partnership
Mexico and Chile are both among the 11 countries in negotiations for the TPP - Chile's President Sebastian Pinera is closely aligned with Mr Key on the talks but a change in leader can mean a change in the country's stance on it - and Mexican President Peno Nieto was only elected last December. Mr Key will be the first foreign leader to hold a bilateral with Mr Nieto and sound out where he stands.
Security Council seat 2015/16
Mr Key will use the visit to lobby for the four countries' votes for New Zealand to secure a seat on the Security Council in 2015/16. Turkey and Spain are contesting the same seat - and the elections for it will be held next year. Although it is convention for countries not to publicly reveal who they will support, Mr Key said three of the four countries he would visit had already indicated they would support New Zealand - and he would be trying to shore that up. "You never know until they vote."
He said Latin America was an important voting bloc. Brazil has been pushing since at least 2009 to secure a permanent seat on the Security Council, arguing its size and economic heft justifies it. New Zealand has pushed for reform of the Security Council, including limits on the veto rights held by permanent members.
It's business time
Mr Key will have a delegation of about 22 business people with him, looking for trade opportunities. Although they include the "big players" such as Zespri and Fonterra, which has a farm in Chile, Mr Key will visit, the majority are niche agri-technology companies.
He said that was because the countries concerned were big producers of beef and lamb themselves so did not provide the same opportunities as countries such as China.
The biggest value was in agricultural services, technology, international education, air services and technology companies.
Those smaller business delegates range from the makers of a machine to sort out soft-skinned fruit such as blueberries by colour, to a satellite and communications systems developer which services the US Army and the Colombian Army.
Education
Chile, Brazil and Colombia are the biggest Latin American markets for international students coming to New Zealand - especially at a secondary school level, when many students travel to an English-speaking country. Education NZ will be on the trip, as well as the Manukau Institute of Technology, trying to increase the numbers of tertiary students.
