The two companies have been in negotiations for several weeks and, according to people familiar with the situation, are discussing the terms of a potential cash and stock deal that would value the business at close to $5 billion. The people cautioned that the talks were ongoing and no deal was certain, however.
European consumer groups, including Nestlé and Fresenius, had been identified as prospective buyers for Danone's medical nutrition business, which makes baby food and the Nutricia and Cow & Gate formula brands. It is unclear if either party is still interested in buying the business.
Illinois-based Hospira, which had a market value of $8.64 billion at Friday's market close, could use an acquisition of the Danone business to redomicle its tax headquarters in France in a deal known as a tax inversion.
To qualify for the inversion, at least 20 per of the shares in the combined company would need to be held outside the US, meaning Hospira, which has a big intravenously delivered nutrition division, would need to fund a large proportion of any bid with its own stock.
The practice has come under intense scrutiny from Washington in the past month, with US President Barack Obama on Thursday labelling companies seeking to redomicle their tax bases as "corporate deserters" who were "technically renouncing their US citizenship".
Danone, the world's largest yogurt-maker by sales, has been working on the sale of the medical nutrition business with JPMorgan, the investment bank, for some months.
The company has struggled in recent years as it has faced challenges in parts of its European business and also Asia, where sales of its infant milk formula were hit by a product recall after a Danone supplier raised a false alarm about its products.
The Paris-based dairy producer last week reported a 20 per cent fall in first-half operating profit as the group battled high milk prices, a strong euro and the fallout from the product recall in Asia.
Analysts at Natixis said last week that the company "continues to disappoint the market. While the stock has underperformed its peers by 13 per cent over the last 12 months, the current situation has been criticised for numerous reasons: a lack of sincerity on 2014 targets, poor execution quality, high M&A risk and weak value creation for the shareholder".
They added that the company must make significant cultural and managerial changes to achieve improved profitability and reduce the risk of a takeover bid by rivals including Read MorePepsiCo and Nestlé.
Danone and Hospira were not immediately available for comment.
—By Ed Hammond and Arash Massoudi; Additional reporting by Scheherazade Daneshkhu in London and Adam Thomson in Paris