Kroenke, whose sporting empire includes American football team Los Angeles Rams and basketball's Denver Nuggets, has bought a majority share in Bonneau du Martray, a history-soaked wine grower in France's Burgundy region, business newspaper Les Echos reported.
The newspaper did not reveal the price of the buyout, and the family which owns the site, the Le Bault de la Morinieres, could not be reached Wednesday evening.
Regional industry body BIVB said it had not been informed of the decision.
Kroenke, pictured above (right), with his son. Photo: AFP
Most of the red and white grand cru wines produced on Bonneau du Martray's 11-hectare site are destined for export, ending up on the tables of expensive restaurants.
Kroenke, a publicity-shy 69-year-old who is married to Wal-Mart heiress Ann Walton Kroenke, already has Californian vineyards in his business empire in the form of Napa Valley's Screaming Eagle.
Screaming Eagle's estate manager Armand de Maigret, quoted by Les Echos, said Kroenke's first foreign acquisition in the wine-making world was "the product of love at first sight".