In the latest report for La Nacion, the paper quotes Santa Fe Production Minister Luis Contigiani as saying August would be a key month to define the fate of SanCor.
The paper also said a number of auditors were looking at SanCor's accounts for a possible purchase.
The report estimated the likely price tag for SanCor oscillates between US$200m and US$400m. Fonterra already has extensive interests in Latin 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.