By Cara Lombardo and Annie Gasparro

Kraft Heinz Co. is nearing a deal to sell a big chunk of its cheese business to France's Groupe Lactalis SA for about $3.2 billion as the struggling U.S. food company seeks to jump-start growth in its other businesses, according to people familiar with the matter.

The deal is expected to be announced Tuesday, the people said, assuming there isn't a last-minute hitch. The transaction involves Kraft Heinz's natural-cheese business and consists of a mix of brands in the U.S. and Canada and the company's cheese business outside of North America, some of the people said.

Kraft Heinz has struggled in recent years with consumers defecting to foods that seem trendier or healthier and the pressure to revive sales has tempered its ability to improve profitability. That is reflected in a stock that has lost more than half its value and now gives the company a market capitalization of about $40 billion, not much more than its debt load of nearly $30 billion. Some proceeds from the sale are earmarked for debt reduction, one of the people said.

Kraft is holding a virtual meeting with its investors on Tuesday and already announced it plans to cut $2 billion in costs over five years, returning to the strategy that inspired the company's formation in a merger five years ago.

Closely held Lactalis, a global dairy company based in France, produces brie, ricotta and other cheeses in the U.S. and sells them under brands including President.

The company, which entered the U.S. about 40 years ago, has been on an expansion spree here, acquiring Stonyfield organic yogurt from Danone SA in 2017 in a deal valued at $875 million.

Adding the Kraft cheese business would boost the company's footprint further at a time when demand for staple groceries is higher than ever amid the coronavirus pandemic.

Write to Cara Lombardo at cara.lombardo@wsj.com and Annie Gasparro at annie.gasparro@wsj.com