* Talks start after Bountiful announces plan to float

* Analysts estimate price tag of $5-$7 billion

* Deal would be latest Nestle acquisition in nutrition

ZURICH, April 26 (Reuters) - Nestle is in talks to buy nutritional supplement maker The Bountiful Company, the Swiss food giant said on Monday, as it looks to move further into a health and nutrition sector that is growing faster than its traditional packaged food business.

Analysts expect a price tag of $5-$7 billion for Bountiful, which makes Nature's Bounty vitamins, Osteo Bi-Flex joint-care supplements and Puritan's Pride vitamins and supplements, but Nestle in its statement gave no indication of a price.

The acquisition would fit with the M&A strategy of Chief Executive Mark Schneider, the former Fresenius boss who has targeted several health companies since taking charge at Nestle in 2016.

"Nestlé S.A. today announced that it is in discussions to acquire all or part of The Bountiful Company," Nestle said, confirming media reports but giving no further details.

Separately, Knorr soup maker Unilever said on Monday it would buy food supplements maker Onnit.

Nestle's approach for Bountiful, which is majority-owned by private equity firm KKR Co & Inc, came after Bountiful filed for a New York Stock Exchange flotation this month.

In 2020, Long Island-based Bountiful had sales of $2.07 billion, 10% higher than a year earlier. It increased its adjusted earnings before interest, tax, depreciation and amortization by 21% to $302.3 million.

In its 2019 results, before the pandemic struck, Nestle increased reported sales only by 1.2%, held back by sluggish performances in water, confectionary and prepared dishes.

"This is about diversifying the growth profile in Nestle and trying to get growth in areas other than coffee and pet care," said Bank Vontobel analyst Jean-Philippe Bertschy, who said a move for Bountiful made strategic sense for the world's largest packaged food company.

In the past five years, nutritional food sales have increased by an average of 5.8% per year, faster than the 4.7% rate of packaged foods, according to Euromonitor data.

Only 17% of the estimated $137 billion in annual global sales in nutritional food are generated in Europe, Middle East and Africa, offering scope for further expansion in the region.

Meanwhile, 17% of Bountiful's sales come form e-commerce, a faster growing retail channel than shops, while Nestle could leverage its distribution and marketing to increase sales further.

"I think the health and wellness area will continue to be the focus of Nestle's M&A activity, because of the faster growth and higher returns," said Bertschy.

(Additional reporting by Siddharth Cavale. Editing by Susan Fenton and Mark Potter)