The Swiss group had already been seen as favourite for the business, and is now set to seal a deal later this month after outbidding a joint team of Danone
Nestle is in the lead position and is closing in on a deal which we expect soon, said one source.
Another source said the business would fetch $9-$10 billion and expected a deal by the end of the April.
If Danone loses out, analysts say the French group will face a problem of how to expand, with its Chief Executive Franck Riboud saying it did not have the firepower to mount big deals which would seem to rule out an eventual move for Mead Johnson.
The Pfizer unit is a high-growth $2.1 billion turnover business with over 70 percent of sales in emerging markets and a key position in China, and has attracted the attention of the three largest players in the infant milk formula sector.
Pfizer put the business up for sale last July following its $68 billion purchase of Wyeth in 2009, while it is also looking to offload its animal health business and says this is more likely to be spun off than sold outright.
A spokesman for Vevey-based Nestle, which holds its annual general meeting in Lausanne on Thursday and releases first-quarter sales figures on Friday, said we never comment on market rumours.
Analysts said if the deal is concluded it would be positive for Nestle and also may help Danone's shares as there has been concern that the French group might pay a huge price for the business and massively leverage up its balance sheet.
Overall, this deal makes huge strategic sense for Nestle. It is in the right categories and the right markets and with a reasonable price we would expect a fairly positive response from investors, said analyst Andrew Wood at Bernstein.
Nestle shares were off 0.3 percent at 56.60 Swiss francs and Danone up 1 percent at 53.61 euros by 10.30 a.m. British time.
WORLD NUMBER 5
The Pfizer business with its SMA Gold brand ranks as world number five in the infant milk formula market - the world's fastest growing packaged food category - after Nestle, Mead Johnson, Danone and Abbott Laboratories
It is currently growing sales at 8 percent a year and has some 60 percent of its revenue in Asia, 30 percent in Europe, largely in Britain, and some 10 percent in Latin America.
Over a quarter of its sales are in China, where the $6 billion market is expected to double by 2016 having grown at more than 20 percent over the last five years to feed 16 million new births a year. A Pfizer deal would push Nestle to No 3 in the Chinese market behind Mead Johnson and Danone from its current relatively small presence.
Nestle, whose main baby milk brand is NAN, is likely to have to sell 25 percent of the Pfizer unit's sale by disposing of interests in Latin America, south east Asia, Australia and South Africa, which analysts say could be bought by Danone or Heinz
Danone has always declined any comment, but Riboud said in February he was interested in acquisitions but did not have the firepower for deals on the scale of its 12.3 billion euro ($16.2 billion) acquisition of baby food group Numico in 2007.
Mead Johnson share closed on Tuesday at $83.61 giving it a market capitalisation of around $17 billion, making it a potentially more expensive acquisition than Numico.
If Nestle pays $10 billion for the Pfizer business it would be on a similar 22 times multiple of core EBITDA profit that Danone paid for Numico and ahead of the 15.7 times Nestle paid for babyfood group Gerber in a $5.5 billion deal in 2007.
On Tuesday, the Wall Street Journal reported that Pfizer is near to selling the business to Nestle for at least $9 billion in a deal that could be announced as soon as next week.
The auction is being run out of New York with Morgan Stanley and Centerview Partners advising Pfizer.
($1 = 0.7610 euros)
(Editing by Hans-Juergen Peters)