"In the end it is the American General Mills that will acquire Yoplait," the French daily wrote without citing its sources.
Neither Yoplait or PAI, nor Sodiaal which owns the other 50 percent in Yoplait, was immediately available for comment.
Yoplait is present in 50 countries and has global sales of some 4.0 billion euros, and trails only French rival Danone.
General Mills, one of the world's largest food companies with $16 billion in sales last year and which already distributes Yoplait products in the United States, would gain a majority as Sodiaal is to sell a one percent stake as part of the deal.
A number of companies are believed to have been interested in buying the stake in Yoplait, including Switzerland's Nestle and China's Bright Food Group.
Le Figaro reported last month that Bright Food had tabled the highest bid so far for PAI Partners' 50 percent stake in Yoplait, valuing the French firm at around 1.7 billion euros.
"Societe Generale which is in charge of the sale has told us that the deal has not been signed yet," a Bright Food spokesman told AFP.