The companies would likely develop health-focused beverages that will ease inflammation, pain and cramping, the report said, citing sources familiar with the matter.
"Along with many others in the beverage industry, we are closely watching the growth of non-psychoactive CBD as an ingredient in functional wellness beverages around the world," Coca-Cola said in a statement, referring to cannabidiol, a constituent of cannabis.
"No decisions have been made at this time," the beverage group said, adding that it would not comment on further speculation.
Aurora, in a separate statement, said it would not discuss business development initiatives until they are finalized, but added: "Aurora has expressed specific interest in the infused beverage space, and we intend to enter that market."
A partnership between Coke and Aurora would mark the first entry of a major manufacturer of non-alcoholic beverages into the market for cannabis-related products.
There is no guarantee that talks between the companies will be successful or that a commercial agreement would be made public, BNN Bloomberg reported.
Earlier this year, alcohol producer Molson Coors Brewing said it will make cannabis-infused drinks with Hydropothecary, while Corona beer maker Constellation Brands invested $4 billion more into marijuana producer Canopy Growth.
Coca-Cola's shares rose marginally in pre-market trade on Monday.