The company was interested in buying the entire business, which had $6.7 billion (€6.3 billion) in revenue last year, and "not just... a few vessels", The Wall Street Journal reported on Monday, citing a person familiar with the matter.
"Out of principle we do not comment on rumours," Maersk said in an email to AFP on Tuesday.
Hamburg Sud's owner, the family-owned Oetker Group, was discussing a sale of its shipping business, the same newspaper reported last week.
"Hamburg Sud is one of the players in the industry that is probably too small to survive in the long run. It only has three percent of the market," Sydbank analyst Morten Imsgard told Danish news agency Ritzau.
The shipping industry is undergoing a wave of consolidation after suffering its worst downturn in six decades amid overcapacity and slumping global trade.
Japan's three largest shipping firms said in October they were merging their container businesses, and France's CMA CGM earlier this year bought Singapore-based container liner Neptune Orient Lines (NOL).
Hanjin -- South Korea's largest shipping company and once the world's seventh biggest -- filed for bankruptcy protection in August.