But the discussions have for now been put on hold and it remains unclear if the proposed deal and its structure could be revived, people familiar with the matter said this week, asking not to be named because the matter is not public.
It was not immediately clear why the parties paused discussions, but the decision comes as U.S. companies considering tax inversions come under intense pressure from the government and politicians to rethink their plans.
When Hospira's interest in the Danone business first emerged in July, a senior U.S. senator wrote to the Lake Forest, Illinois-based company urging it not to move its tax base abroad.
Read More Hospira in talks to buy Danone medical nutrition arm
Dick Durbin, the No. 2 Democrat in the Senate, represents Illinois and he told Chief Executive Michael Ball that Hospira should not "turn its back on American taxpayers and consumers by taking advantage of a tax loophole called 'inversion."
Reuters first reported in February that Danone, the world's biggest yogurt maker, was considering selling the business—which makes feeding tubes, foods and drinks for people with special nutritional needs—even though it has a profit margin above the group average. Hospira was among a field of bidders including German healthcare group Fresenius and Swiss food company Nestle that also held talks with Danone over the business.
It could not be ascertained if there was another bidder involved in the auction, but one person said the sale process was still ongoing. While talks with Hospira have stalled for now, any potential deal with the U.S. company does not necessarily have to be predicated on a tax inversion, that person added. "All options are still open. Price, structure and bidder—those are uncertain."