DANONE 
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Talks over the business, which has been valued at 4 billion euros ($5.5 billion), would soon enter a decisive phase, they said.
Four groups including Nestle and Fresenius had previously shown interest in buying the business, French daily Les Echos said last month.
Reuters reported in February that Danone, the world's biggest yoghurt maker, was considering selling the business - which makes feeding tubes and foods and beverages for people with special nutritional needs - even though it has a profit margin above the group average.
The company is most likely to use the proceeds from a sale to fund an expansion of its faster-growing baby food and dairy businesses, targeting acquisitions in Asia and Africa, analysts say.
Danone, Nestle and Fresenius all declined to comment.
Nestle, owner of the Nespresso, KitKat, Perrier and Maggi brands, has bought outright the dermatology joint venture it had with L'Oreal and is already a big player in the medical nutrition market.
It has signaled it might move further into healthcare, where growth prospects and profit margins are more enticing than in its traditional food markets.
Fresenius, for its part, has said it is ready for bigger deals after buying hospitals worth 3 billion euros from Rhoen-Klinikum. The Danone business would complement its Kabi business, which makes tube feeding and intravenous feeding equipment as well as generic infusion drugs.
ANTITRUST ISSUES
Warburg Research analyst Ulrich Huwald said Fresenius generated enough cash flows to fund a deal without raising its equity capital and that a transaction would help diversify both Fresenius and its Kabi unit.
"So far the division has been reliant to a large extent on intravenous generic drugs in the United States," he said.
But industry experts have said that either suitor would have considerable antitrust issues to address, making it likely that knock-on deals would follow in markets where the buyer would become too dominant.
Danone's medical nutrition brands include Neocate, a range of replacement formulas for infants allergic to cow's milk, and Nutrini energy drinks for children with faltering growth.
For the $30 billion medical nutrition market as a whole, about three-quarters consists of products delivered orally or through a feeding tube, according to analysts from Exane BNP Paribas.
That portion of the market is led by Abbott Laboratories, with a 30 percent share, followed by Nestle with 25 percent and Danone with 16 percent.
Smaller players include Fresenius and Mead Johnson Nutrition.
The remainder of the market is in nutrition delivered intravenously, and is dominated by Baxter International, Fresenius, B Braun Melsungen and Hospira.
($1 = 0.7291 euros)
(Additional reporting by Dominique Vidalon and Martinne Geller; Writing by Ludwig Burger; Editing by Arno Schuetze and Pravin Char)
By Anjuli Davies and Andreas Kröner
