Fonterra has been in talks with Argentine dairy group SanCor, according media reports from Buenos Aires.
In response to a query from the Herald, the New Zealand co-operative said it did not comment on rumour.
Argentina's two biggest newspapers La Nacion and Clarín carried reports that said Fonterra had been in talks with SanCor.
They said a teleconference is scheduled for this Thursday and Friday (Argentine time) between the respective executives and that Fonterra had visited Argentina in the last two weeks to discuss a deal.
A translation of a report in La Nacion said the family-owned French dairy group Lactalis had also expressed an interest in SanCor.
The paper said SanCor had been valued by an international consultant at US$1 billion ($1.36b) but that it had debt representing 40 per cent that amount.
"As a floor they will seek to cover the value of the debt, but the eventual sale is not going to be close to the international value set by the consultant," La Nacion reported a source close to the negotiations as saying.
"These days there will be a conference call with Fonterra officials where it is going to decide if this progresses or not," the source said.
Fonterra would have presented "harsh conditions" to negotiate, the paper said.
If the option is not to be advanced with the New Zealand firm, contacts with Lactalis would be reactivated. "Progress is still not significant," said another source.
Fonterra already has extensive interests in South America.
In Chile, the dairy giant Saprole is Fonterra's oldest offshore investment, and is the best known corporate brand outside of Coca Cola.
Fonterra is also a significant player in the US$26 billion year dairy market in Brazil.
A Bloomberg profile of SanCor described it as a dairy farmers co-operative, engaging in the production and sale of milk-based products in Argentina and internationally.
It offers skim milk powder, natural or salt butter, gouda cheese, edam, and cheddar. The company was founded in 1938 and is based in Sunchales, Argentina, Bloomberg said.